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

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### 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

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