Question

A teacher has to choose the maximum different groups of three students from a total of
six students. Of these groups, in how many groups there will be included in a particular
student?
12
10
8
6​

Answer 1

Answer:

10

Step-by-step explanation:

Suppose any particular student is always selected.  

Now, the remaining 2 students are to be selected out of the remaining 5 students.

It can be done in 5c2  

 ways =10

Answer 2

The correct answer is 10.

Given :

Total number of students= 6

Number of children in 1 group = 3

TO FIND:

Number of which in which 1 particular student will be included.

SOLUTION:

Number of ways of selecting 3 students from 6 students = 6C3

APPLYING THE FORMULA TO FIND OUT THE COMBINATION :

ncr = n!/ r!(n-r)!

6C3 = 6!/3!(6-3)!

= 6 × 5 ×4× 3 /3 × 3× 2× 1

= 20 groups

similarly, Number of ways. of selecting 2 students from 5 students

= 5!/2(5-2)!

= 5!/2! ×3!

= 5× 4×3×2! / 2! × 3× 2 ×1

= 10

Hence, 10 groups will be there that will include a particular student

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