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
Answers
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
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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