Question

what are the number of ways in which three balls can be simultaneously selected from 16 pool balls where the pool balls have been distinctly numbered from 1 to 16

Answer 1

The number of ways are 560.

Answer 2

There are 3,360 different ways that 3 pool balls could be arranged out of 16 balls

Given:

Balls to be selected = 3

Total number of balls = 16

To Find:

The number of ways in which three balls can be simultaneously selected from 16 pool balls

Solution:

Let the number that can not be selected be = 14

Therefore,

The first choice has 16 possibilities, and our next choice has 15 possibilities, then 14, 13, etc.

Thus,

The total permutations will be -

16 × 15 × 14 × 13 × .....

= 20,922,789,888,000

So now, we need to select only three of them, so that will be only -

16 × 15 × 14 ( Simultaneously)

= 3,360

Answer: There are 3,360 different ways that 3 pool balls could be arranged out of 16 balls

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