Question

If a deck of cards contains 52 cards, then in how many ways can 4 kings be taken out from the deck?

• A. 541450
• B. 270725
• C. 2165800
• D. 1082900

Answer 1

The correct option is B 270725

A deck of cards contains 52 cards.

A deck is shown below.

So, we observe that there are 4 kings in the deck.

The order does not matter here as 4 kings can be taken out in any manner. So, this becomes a combination problem.

${}^n{C}_r=\frac{n!}{(n-r)!\times r!}$

∴ Number of ways in which 4 kings can be taken out of 52 cards
$={}^{52}{C}_4=\frac{52!}{(52-4)!\times 4!}=\frac{52!}{48!\times 4!}$

$=\frac{52\times 51\times 50\times 49\times 48}{48!\times 4\times 3\times 2\times 1}$

$=\frac{52\times 51\times 50\times 49}{4\times 3\times 2\times 1}$

$=13\times 17\times 25\times 49$

$=270725$