n crayon box contains 2 green, 3 yellow and 4 blue crayons. In how many ways can one choose 3 crayons so that at least one yellow crayon is included?

Q: In how many ways can 2 pizza toppings be chosen from 12 available toppings? Your answer is :

A: Consider the formula for the n objects taken r at a time is, Cn,r=n!r!n-r! Then, the number of ways…

Q: In how many ways can 2 pizza toppings be chosen from 12 available toppings?

A: We have given that 2 pizza toppings be chosen from 12 available.

Q: How many two-digit numbers can be formed from the digits 2, 4 and 6 if a. no digit is repeated in…

A:

Q: uppose we want to choose 2 colors, without replacement, from the 4 colors red, blue, green, and…

A: Given we want to choose 2 colors, without replacement, from the 4 colors red, blue, green, and…

Q: In how many ways can we arrange 3 boys and 3 girls in a circular table if:  All boys and girls are…

A: Given, 3 boys and 3 girls       To find, In how many ways can we arrange them if all boys and girls…

Q: How many ways can 5 bicycles be parked if there are 9 available parking spaces?

A: Number of ways in which 5 bicycles can be parked if there are 9 available parking spaces.

Q: How many ways are there to seat six boys and eight girls in a row of chairs so that no two boys are…

A: See the attachment

Q: There are 10 boys and 6 giris. How many ways are there of forming a group of either 3 boys or…

A: We have given that  There are 10 boys and 6 girls. Total number of girls and boys = 16   Combination…

Q: How many numbers greater than 3000 can be form with the digits 0,2,3,4 a.  if repetition is not…

A:

Q: a family wants to adopt 2 cats and 3 dogs from a shelter that has 12 cats and 15 dogs. in how many…

A: The number of ways of selecting 2 cats from 12 cats is,

Q: B. In how many ways can 2 red beads, 3 blue beads, 2 yellow beads, and white beads be arranged in a…

A: Given: Red beads= 2 Blue Beads = 3 Yellow Beads =2   5). Therefore by circular permutations, since…

Q: How many ways can 6 ladies be seated in a circular table such that 2 of the ladies must always sit…

A: To find: The number of ways to arrange 6 ladies in a circular table such that 2 of the ladies must…

Q: In how many ways can a person order one ice cream cone with 3 different flavors of ice cream if…

A:

Q: . How many ways can 3 oranges be chosen from a fruit bowl that contains 11 oranges?

A: We are asked to find the number of ways to choose 3 oranges from 11 oranges

Q: How many ways can 4 books be arranged on a shelf if the books are selected from a collection of 100…

A: Here we will use the concept of permutation Permutation = nPr = n!/(n-r)!

Q: A bag contains 6 red balls and 4 white balls. In how many ways can one draw: 2 balls of different…

A: Given data, Number of red balls=6 Number of white balls=4 In how many ways can one draw 2 balls of…

Q: In how many ways can you place 9 different books on a shelf if there is space enough for only 5…

A: Given, 9 different books on a shelf and there is space only for 5 books.

Q: Suppose we want to choose  3  colors, without replacement, from the  4  colors red, blue, green, and…

A: It is given that there 4 colors red,blue,green and purple.  and we need  to choose 3 colors without…

Q: How many ways can 3 runners be selected for the Olympics from a field of 5 contestants?

A: Number of ways in which X runners can be selected for the Olympics from a field of N contestants is…

Q: How many ways can all the letters in the word EDUCATION can be arranged if all the vowels are right…

A:

Q: An individual is going to paint the 5 toes of their right foot using one or two, but not three of…

A: An individual is going to paint the 5 toes of her right foot using one or two, but not three of the…

Q: Six men and eight women are to line up for a picture with the six men in the middle. How many ways…

A: Given that  Six men and eight women are to line up for a picture with the six men in the middle  How…

Q: ay be formed using the digits 2, 3, 4, 6 and 9 if repetitions

A: 22,23,24,26,29,32,33,34,36,39,42,43,44,46,49,62,63,64,66,69,92,93,94,96,99. In unit digit place we…

Q: On the first day of the Minnesota state fair 1 person enters through the gate in the first minute,2…

A: To find: The number of people enters through the gate in seventh minute. Given: The number of people…

Q: How many different license plates are possible if each contains 3 letters (out of the alphabet's 26…

A: The objective is to find different possible license plates if each contains 3 letters followed by 2…

Q: How many ways can the 7 flowers be chosen?

A: We have given that  Total number of flowers = 18

Q: 3. A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be…

A:

Q: Nine men and six women are to line up for a picture with the nine men in the middle. How many ways…

A: It is provided that there are nine men and six women who are line-up for a picture with the nine men…

Q: Suppose that a bake shop Has four different kinds of cookies. How many different ways can six…

A: We are choosing 6 cookies, i.e r = 6 and  we need 4 different kinds of cookies, i.e n= 4

Q: Is 10 appetizers, 5 maln courses, and 11 desserts. A customer is to select 3 appetizers, 3 main…

A:

Q: There are 6 runners in a race. In how many ways can 3 runners finish in first, second, and third to…

A:

Q: In how many ways can 8 different pizza toppings be chosen from 14 available toppings? There are ways…

A:

Q: You are ordering an extra large pizza with multiple toppings on it. In how many ways can 8 different…

A:

Q: Suppose we want to choose 3 colors, without replacement, from the 4 colors red, blue, green, and…

A: Permutation and combination

Q: 9) License plates are made using 3 letters followed by 3 digits. How many plates can be made if…

A: Permutation and combination used to calculate the number of possible ways to arrange or select a…

Q: In how many ways can this be done if the three adults are seated together and the five children are…

A: Given Information: There are 3 adults and 5 children. They are to be seated randomly in a row. Three…

Q: 3. How many 4- digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 it: a) no…

A: Given many 4-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7

Q: There are 12 different books in a bag. In how many ways can we take 4 books from the bag and stack…

A: From the provided information, There are 12 different books in a bag and 4 books taken from bag.

Q: A committee of 3 is to be formed from a group of 20 people. How many different committee are…

A: A committee of 3 is to be formed from 20 people. So there has to be 3 selections from 20 people…

Q: Five couples want to have their pictures taken. In how many ways can they arrange themselves in a…

A: Given: Five couples want to have their pictures taken. In how many ways can they arrange themselves…

Q: In how many ways can 2 pizza toppings be chosen from 12 available topping Your answer is :

A: Given : n = 12  r = 2

Q: four crayons be chosen from a bo

A: The selection of elements without arrangement can be represented by a combination of elements.…

Q: 3. In a box, there are 5 black pens, 3 white pens and 4 red pens. In how many ways can 2 black, 2…

A: Answer: In 180 ways 2 black , 2 white, and 2 red pens can be chosen.

Q: Natasha and Rodrigo are in a class of 30 students that selects 4 leaders. How many ways are there to…

A: Solution:

Q: How many different arrangements of 4 letters can be formed if the first letter must be W or K…

A: Total no.of letters(A to Z)=26

Q: 3. Copy Central prints black and white or colored copies. Yesterday, they printed 9 black and white…

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

Q: In how many ways can 16 different pizza toppings be chosen from 20 available toppings? There are…

A:

Q: A family has 6 kids. In how many ways could the parents have the three boys and three girls?

A:

Q: How many ways are there to seat 6 different boys and 6 different girls along one side of a long…

A: Given that, there are 12 persons and 12 seats. 12 persons includes 6 boys and 6 girls. Therefore,…