Home
Class 12
MATHS
In how many ways can a team of 6 horses ...

In how many ways can a team of 6 horses be selected out of a stud of 16, so that there shall always be three out of A B C A B C, but never A A, B B or C C together

A

720

B

840

C

960

D

1260

Text Solution

Verified by Experts

The correct Answer is:
C
`because`16 horses=10 horses+(A,B,C,D,E,F)
`therefore`The number of ways`=.^(10)C_(3)xx`(Number of ways of ways of choosing out of A,B,C,D,E,F, so that AD,BE and CD are not together)
`=.^(10)C_(3)xx`(One from each of pairs AD,BE,CF)
`=.^(10)C_(3)xx.^(2)C_(1)xx.^(2)C_(1)xx.^(2)C_(1)=960`
Promotional Banner

Similar Questions

Explore conceptually related problems

In how many ways can a team 11 players be formed out of 25 players, if 6 out of them are always to be included and 5 always to be excluded

If A ,B and C be three sets such that A uu B = A uu C and A nn B =A nnC , then :

Show that if A ⊂ B , then C – B ⊂ C – A .

In how many ways can a cricket team of eleven players be chosen out a batch 15 players, if (i) a particular player is always chosen. (ii) a particular player is never chosen?

Let A, B, C be three events. If the probability of occurring exactly one event out of A and B is 1 - a, out of B and C is 1 - 2a, out of C and A is 1 - a and that of occuring three events simultaneously is a^(2) , then prove that probability that at least one out of A, B, C will occur is greater than 1/2.

If A,B and C are three sets such that A nn B= A nn C and A uu B=A uu C , then :

Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C . Show that B = C .

If A ,B and C are any three sets , then A x (B uu C ) is :

Find the number of ways to give 16 different things to three persons A, B, C so that B gets 1 more than A and C gets 2 more than B.