A standard deck of cards 52 cards has 13 ranks R={A,2,3,4,5,6,7,8,9,10, J, Q, K}and four suits S={♥,♦,♣,♠}. Now, we play cards with an extended deck. We have an additional suit of cards: the dollar suit $ ; and an additional rank: Price . For example, the “Price of dollar” card is P$ a) Write the following sets: S′= the suits of the new deck & R′= the ranks of the new deck b)Which cards are in the new deck that are not in the standard deck? (i) Write your answer as a set using R, S, R′, S′and the set operations:× \ ∪ { }. (ii) List the elements which are in the new deck, but not the standard deck. c) How many cards are there in the new deck which are not in the standard deck?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Q1:
A standard deck of cards 52 cards has 13 ranks R={A,2,3,4,5,6,7,8,9,10, J, Q, K}and four suits S={♥,♦,♣,♠}. Now, we play cards with an extended deck. We have an additional suit of cards: the dollar suit $ ; and an additional rank: Price . For example, the “Price of dollar” card is P$
a) Write the following sets:
S′= the suits of the new deck & R′= the ranks of the new deck
b)Which cards are in the new deck that are not in the standard deck?
(i) Write your answer as a set using R, S, R′, S′and the set operations:× \ ∪ { }.
(ii) List the elements which are in the new deck, but not the standard deck.
c) How many cards are there in the new deck which are not in the standard deck?
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