Aptitude - Permutation and Combination - Discussion

Discussion Forum : Permutation and Combination - General Questions (Q.No. 6)
6.
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
159
194
205
209
None of these
Answer: Option
Explanation:

We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).

Required number
of ways
= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)
= (6 x 4) + 6 x 5 x 4 x 3 + 6 x 5 x 4 x 4 + 6 x 5
2 x 1 2 x 1 3 x 2 x 1 2 x 1
= (24 + 90 + 80 + 15)
= 209.

Discussion:
92 comments Page 8 of 10.

GunaVel said:   10 years ago
Any another easy method?

Nikhil said:   10 years ago
Actually one need not use nCr=nC (n-r) concept. Just use the concept that nCr= n!/(r!* (n-r) !). You will get the answer.

Sarasa said:   10 years ago
Why didn't nC (n-r) method use for 6c2? Anyone please explained it?

I didn't get answer for this.

Galla said:   1 decade ago
Wow your various explanations really did help.

Atul said:   1 decade ago
I am not satisfied from the above ways because I don want to use simpler method.

Tell me why did we apply formula only on 1st and last terms. Why not on other terms?

Srinivas said:   1 decade ago
Can any one explain how we apply formula ncr = nc(n-r) to only first and last term only?

Mayur said:   1 decade ago
One Question has many times came no one gave answer.

Why formula use for only first term ncr(n-r)?

Why not for other one, how can we know when we use this formula?

Maggi said:   1 decade ago
In 1st step :........+ (6c1 x 4c3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4).

In 2nd step :........+ (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2).

If we use formula nC(n-r) then it is not applied to 6C2 x 4C2. So on.

Shilpa said:   1 decade ago
6c2= 6!/2!(6-2)!

= 6!/2!*4!
= 6*5*4! 2*4!

Then 4! will be cancel.
= 6*5/2.

By solving it.
= 15 got in result.

Shreu said:   1 decade ago
But the also there the children how it is possible?


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