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Question

In how many ways 8 people can be divided into two groups of 5 and 3 people?

A
3136
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B
56
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C
560
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D
1
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Solution

The correct option is B 56
Total number of people =8
Number of people in first group =5
Number of people in second group =3

The first group of 5 people can be selected from 8 people in 8C5 ways.

8C5=8!5!(85)!

8C5=8!5!3!

8C5=56


The first group of 5 people can be selected from 8 people in 56 ways.

Now, we are available with 85=3 people as 5 people are already selected in the first group.

We need to select 3 people from the 3 available people to form the second group.

The second group of 3 people can be selected from 3 people in 3C3 ways.

3C3=3!3!(33)!

3C3=3!3!0!

3C3=1 (0!=1)

Total number of ways in which 8 people can be divided into group of 5 and 3 people:
=56×1=56

Therefore, option (b.) is the correct answer.

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