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?
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 numberof ways |
= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4) | |||||||||||||||||||
| = (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2) | ||||||||||||||||||||
|
||||||||||||||||||||
| = (24 + 90 + 80 + 15) | ||||||||||||||||||||
| = 209. |
Discussion:
92 comments Page 6 of 10.
Aniket said:
7 years ago
@All.
6c4 = 6c2.
Because 6c4= 6!/(4!*2!) and 6c2=6!/(2!*4!) both are same that's why 6c4=6c2.
6c4 = 6c2.
Because 6c4= 6!/(4!*2!) and 6c2=6!/(2!*4!) both are same that's why 6c4=6c2.
Pranali said:
9 years ago
In first step (6c2 * 4c2).
Send step ( (6*5/2*1) * (4*3/2*1) ).
How?
I can't understand it
Send step ( (6*5/2*1) * (4*3/2*1) ).
How?
I can't understand it
Ash said:
1 decade ago
Why nCr formula is not used here (6C2 x 4C2) , (6C3 x 4C1).?
Can any one explain me this
Can any one explain me this
Gayathri m said:
1 week ago
The second step is not determined.
i.e (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2).
i.e (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2).
Srinivas said:
1 decade ago
Can any one explain how we apply formula ncr = nc(n-r) to only first and last term only?
Sonu said:
9 years ago
Should not we have to arrange all the children? In this we have just make combinations.
Neema said:
9 years ago
Not mention that how many person should we take at a time, the how it will be solved?
Aditya said:
1 decade ago
Hi Pri,
Its because nCr = nC(n-r). So 4C3 = 4C(4-3) = 4C1.
Its one of the formulaes.
Its because nCr = nC(n-r). So 4C3 = 4C(4-3) = 4C1.
Its one of the formulaes.
Nikhil said:
1 decade ago
At least 1 boy = total selections - no boy.
= 10c4-(6c0*4c4).
= 210-1.
= 209.
= 10c4-(6c0*4c4).
= 210-1.
= 209.
Geet said:
1 decade ago
How to use ncr=ncn-r formula?why it is not used in second number 6c2 x 4c2?
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