Question

You deal a pile of cards, face down, from a standard 52-card deck. What is the least number of cards the pile must have before you can be assured that it contains at least five cards of the same suit

Answer 1

we need at least 17 - card deck

Explanation:

From the information given :

We can attempt to solve the question by using pigeonhole principle;

"The pigeonhole principle posits that if more than n pigeons are placed into n pigeonholes some pigeonhole must contain more than one pigeon"

Thus; the minimum number of pigeon; let say at least n pigeons sit on at least one same hole among m hole can be represented by the formula:

m( n - 1 ) + 1

where ;

pigeons are synonymous to card

pigeonholes are synonymous to suits

So; m = 4 ; n = 5

∴ 4 (5 -1 ) + 1 ⇒ 4 (4) + 1

= 16 + 1

= 17

Hence; we need at least 17 - card deck