The number of ways of dividing 52 cards amongst four players so that three players have 17 cards each and the fourth players just one card, is

The number of ways of dividing 52 cards amongst four players so that three players have 17 cards each and the fourth players just one card, is

1. A

$\frac{52!}{\left(17!{\right)}^{3}}$

2. B

52!

3. C

$\frac{52!}{17!}$

4. D

None of these

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

I agree to the terms and conditions and privacy policy.

Solution:

For the first player, distribute the cards in , ways.

Now, out of 35 cards left 17 cards can be put for second player in, ways.

Similarly, for third player put them in , ways. One card for the last player can be put in , way.

Therefore, the required number of ways for the proper distribution

$\begin{array}{l}{=}^{52}{\mathrm{C}}_{17}{×}^{35}{\mathrm{C}}_{17}{×}^{18}{\mathrm{C}}_{17}{×}^{1}{\mathrm{C}}_{1}\\ =\frac{52!}{35!17!}×\frac{35!}{18!17!}×\frac{18!}{17!1!}×1!=\frac{52!}{\left(17!{\right)}^{3}}\end{array}$

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

I agree to the terms and conditions and privacy policy.