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. `840` b. `1260` c. `960` d. `720`

Options

A. 720
B. 840
C. 960
D. 1260

Answer

C

Explanation

`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`