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

we need at least 17 - card deck

Step-by-step 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