Question

You pick cards one at a time without replacement from an ordinary deck of 52 playing cards. What is the minimum number of cards you must pick in order to guarantee that you get a) three of a kind, and b) three Kings. Use the binomial theorem to expand (2x + y)^6. You must illustrate use of the binomial theorem.

Answer 1

Answer:

Three of a kind:

There are a total of 4 sets with 13 cards each.

For three of a kind:

we need to select a minimum of 2*13 + 1 = 26 + 1 = 27 cards.

Three Kings:

There are four kings in a deck of cards. One has to pick 51 cards to guarantee there are three kings. If one picks 48 cards he might mot get even one king. This is the worst possible case

No.of cards to be picked = 51

(2x + y)^6: