Question

how many ways 5 passengers can sit in a compartment having 16 vacant seats
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Answer 1

Answer:

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Answer 2

Given:

5 passengers can sit in a compartment having 16 vacant seats.

To Find:

The ways 5 passengers can sit in a compartment.

Solution:

To find the ways 5 passengers can sit in a compartment we will follow the following steps:

As we know,

For the first passenger, he can sit in 16 ways.

Now, 15 seats are vacant so the next passenger can seat in 15 ways.

Similarly, the next passenger that is third can sit in 14 ways.

Now,

These are making permutation and permutation without repetition is calculated as

$\frac{n!}{r! (n - r)!}× 5!$

5! is added because 5 passengers can arrange themselves in 5! ways.

Here, n is 16 and r is 5

Now, putting values in the above formula we get,

$\frac{16!× 5!}{ 5! (16 - 5)!} = \frac{16 \times 15 \times 14 \times 13 \times 12 \times 11!× 5!}{5! \: 11!}$

Cancelling 5! and 11! both in numerator and denominator.

$\frac{16 \times 15 \times 14 \times 13 \times 12}{1!}$

524160 ways.

Henceforth, the ways 5 passengers can sit in a compartment having 16 vacant seats are 524160.