A lottery game requires that you pick 7 different numbers from 1 to 59. If you pick all 7 winning numbers, you win the jackpot. If you pick 6 of the 7 numbers corectly, you win $300,000. In how many ways can you pick exactly 6 of the 7 winning numbers without regard to order? There are ways to pick exactly 6 of the 7 winning numbers without regard to order.

Q: In a shipment of 10 items where 3 are defective. In how many ways can you receive 4 items where 2…

A:

Q: How many ways are there to arrange 12 identical apples and five different oranges in a row so that…

A: Here, arrange 12 identical apples and five different oranges in a row so that no two oranges will…

Q: In how many ways can a  friend visit his 3  friends  if he must visit all of them in a single day

A: Since, you have asked multiple question, we will solve the first question for you. If you want any…

Q: A restaurant offers a special pizza with any 5 toppings. If the restaurant has 13 toppings from…

A: Combination: The number of different selections of ‘r’ elements (order doesn’t matter) from a set of…

Q: A fair coin is tossed 5 times and the sequence of heads and tails is observed. How many outcomes…

A:

Q: how many ways can you invite at least 7 of your 10 friends?

A: Given that  Total number friends (n) = 10 Number of friends to invite = At least 7    We know that…

Q: In how many ways can a hostess select 6 luncheon guests from 10 women, if she is to avoid having a…

A:

Q: Suppose 15 cars start at a car race. In how many ways can the top 3 cars finish the​ race? The…

A: Permutations: The number of permutations of r items selected from n items is, Prn=n!n-r! In this…

Q: A race has 10 runners. In how many ways can the first three places be decided?

A: Here use combination

Q: 9. How many ordered sets of 3 even numbers are there that will add up to 60? How many different ways…

A: Combinations: The combination is a mathematical method that determines the number of possible…

Q: In a particular lottery, 6 winning numbers are drawn from a group of 55 numbers. The order that the…

A: Given that, there are total 55 numbers and among them winning numbers are 6.

Q: how many ways can Dr. Yes invite 8 of his friends if he has to invite at most 4 at a time?

A:

Q: Three cards are chosen without replacement from a deck of 52 cards and placed in order from first to…

A: In the deck of 52 cards, there are total 4 6's. (One for each of hearts, diamonds, spades and clubs)…

Q: A basketball team has 12 players on it. In how many different ways could a 5-player starting lineup…

A:

Q: How many different ways can you arrange 2 letters from a set of 3 letters {T, S, U} such that…

A:

Q: A bank of 9 movies is chosen from for a movie marathon in which 3 movies will be played in a…

A: Given that,  There are 9 movies in the bank. According to the given condition, 3 movies are played…

Q: In how many ways can you make any arrangement of 3 vowels and 5 consonants taken from the alphabet…

A: In how many ways can you make any arrangement of 3 vowels and 5 consonants taken from the alphabet…

Q: A shipment of 40 computers are unloaded from the van and tested 6 of them are defective In how many…

A: We will find out the required number of ways.

Q: In how many ways can a person select seven party guests from 12 women if he is to avoid having a…

A:

Q: How many ways are there to pick 10 pieces of fruits from a fruit hawker who has four types of…

A: Given information: The number of mangoes in the basket are n(M) = 3. The number of peaches in the…

Q: shows houses to a potential buyer. There are ten houses of the desired price on a list for the area.…

A: Number of ways one could choose three houses from 10 houses, if the order of visit is considered…

Q: In how many ways you can choose 8 of 32 playing cards not considering their order?

A: The combination of a number of objects is their arrangement without considering the order in which…

Q: How many possible ways can the top 5 finishers come in during a race with 24 racers? Each place…

A: This is a permutation problem.   Out of the 24, there will be 5 racers in the top 5.

Q: A student wants to buy 3 CDs. Assume that they are interested in 6 CDs featuring the piano, 4 CDs…

A:

Q: In a particular lottery, 8 winning numbers are drawn from a group of 53 numbers. The order that the…

A: Total numbers of lotteries are 53. The total winning number are 8.

Q: A student wants to buy 3 CDs. Assume that they are interested in 6 CDs featuring the piano, 5 CDs…

A:

Q: A student wants to buy 3 CDs. Assume that they are interested in 6 CDs featuring the piano, 4 CDs…

A: Given Data : Number of Piano CDs are 6                       Number of Trumpet CDs are 4…

Q: A TV game show selects four contestants from an audience of 26 people. If the same 26 people showed…

A: Given: Total number of people=26Number of people selected=4 The permutation formula is applied when…

Q: 7. Suppose you have 15 CDs from which you choose 6 CDs to put in the CD player in your car. If you…

A: As per guidelines expert have to answer first question only dear student please upload other…

Q: A 5-card hand is dealt from a well-shuffled deck of 52 cards. How many ways are there to get a hand…

A: GivenThe number of cards in one deck of cards =52The number of cards in a hand =5 The number of…

Q: In how many ways can a person invite 3 out of their 11 closest friends to a dinner party?

A: Given ,        No of closet friends=11

Q: Alice and Paolo are among 6 candidate for promotion. Suppose there are 4 people who gets promoted…

A: (a) Since, we need to select 4 persons among 6, therefore, the order in which they are going to be…

Q: A student wants to buy 3 CDs. Assume that they are interested in 3 CDs featuring the piano, 6 CDs…

A: In this context, the total number of CDs interest by a student is 14(=3+6+5).a.The number of…

Q: four cards labeled a,b,c and d are randomly placed in four boxes labeled a,b,c, and d. each box…

A: For first card there are 4 choices for next one there will be 3 choices and so on,...

Q: A lottery game requires that you pick 7 different numbers from 1 to 77. If you pick all 7 winning…

A: We have to find the no  of ways given as:

Q: There are 11 songs inside a person's playlist.  If the music is shuffled randomly and they listen to…

A: Given that there are 11 songs inside a person's playlist. If the music is shuffled randomly and they…

Q: Jack is playing with a standard deck of 52 playing cards. He shuffles the cards and then turns the…

A:

Q: How many permutations are there of the letters in the word 'PENCILS', if all the letters are used…

A: If all the letters in the word are distinct and we have to arrange letters without repetition, then…

Q: A hand consists of 4 cards dealt from an ordinary deck of 52 cards. How many hands are there…

A: Solution: The ordinary deck of 52 cards consist of four suits (hearts , diamond, spades, and club)…

Q: A group of 8 people, including Betty and Bob, are going to take a group photo. In how many ways can…

A: Number of people in group is 8 .

Q: From a group of 18 customers, 4 are to be chosen to receive a special gift. Assuming that the order…

A: The number of groups of 4 customers can be chosen is,

Q: Consider a Little League team that has 15 players on its roster. Suppose 6 of the 15 players are…

A: Given information: The total number of players in the team is N = 15. The number of left-handed…

Q: 11. In how many ways can we seat 7 people at a round table with a certain 3 people not in…

A:

Q: In how many ways can a person select seven party guests from 12 women  if he is to avoid having a…

A: Here we will use the concept of Combination

Q: 8. Find the number of different salads consisting of one or more of these vegetables – Tomatoes,…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: . I selected 10 letters fromp a bag of letter tiles. In this case, all ten of the letters are…

A:

Q: Parents are having triplet babies and have put 4 unique name cards in a bowl. * When the first baby…

A:

Q: A shipment of 40 computers are unloaded from the van and tested. 6 of them are defective. In how…

A:

Q: how many are the possible cases, regardless of

A: From the given information, The coin is tosses n times. And the coin has two faces.

Q: In how many ways can 5 starting positions on a basketball team be filled with 8 men who can play any…

A: GivenNo.of Men(n)=8No.of positions(r)=5

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.