Question

Determine the number of different groups of 5 items that can be selected from 12 distinct items.

Answer 1

There are total 95040 number of different groups of 5 items can be selected from 12 distinct item.

According to the given question.

Total number of items, n = 12

Total numbers of items to be selected, r = 5

Since, we have to determine the number of different groups of 5 items that can be selected from 12 distinct items. So, we will find the number of different groups by permulation formula i.e.

$^{n} P_{r} = \frac{n!}{(n-r)!}$

Where,

$^{n} P_{r}$ is the total number of permutations.

n is the total number of objects.

r is teh total number of objects to be selected.

Therefore,

The number of different groups or permutaions of 5 items that can be selected from 12 distinct group

$^{12} P_{5}$

$= \frac{12!}{(12-5)!}$

$= \frac{12!}{7!}$

$= \frac{12\times11\times10\times9\times8\times7!}{7!}$

= 12 × 11 × 10 × 9 × 8

= 95040

Hence, there are total 95040 number of different groups of 5 items can be selected from 12 distinct item.

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