1.

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:(i) exactly 3 girls ?(ii) atleast 3 girls ?(iii) atmost 3 girls ?

Answer» (i) `g=3,b=4`
total ways = `.^4C_3.^9C_4`
`=4*(9*8*7*6)/(4*3*2) = 63*8`
`=504`
(ii) `g= 3 or 4`
total ways =`.^4C_3 .^9C_4 + .^4C_4.^9C_3`
`4*(9*8*7*6*5)/(5*4*3*2) + (9*8*7)/(3*2)`
`= 504+84`
`=588`
(iii)`g=1,2,3`
total ways `= .^13C_7 - .^4C_4.^9C_3`
`= (13*12*11*10*9*8)/(6*3*2*5*4) - 84`
`=143*12- 84`
`=1716- 84`
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