Determine the minimum number of cards which must be selected

Determine the minimum number of cards which must be selected from a standard deck to be sure that at least five of the selected cards have the same suit.

Solution

think of the worst case

you drew some cards and got first 4 of one suit next 4 of different suit and next 8 of different suit

so now you have taken 16 cards all 4 suit and each of 4 cards

now when you will draw any next card you will have one suit with 5 cards

hence answer is 17