If 11 members of a committee sit at a round table so that the president and secretary always sit together, then the number of arrangements, is

Explanation

Number on the faces of the dice are 1,2,3,4,5,6 (least number 1, greatest number 6)
here, l=1, m=6, r=3 and n=15
`therefore`Required number of ways=Coefficient of `x^(15-1xx3)` in the expansion of `(1-x^(6))^(3)(1-x)^(-3)`
=Coefficient of `x^(12)` in the expansion of
`(1-3x^(6)+3x^(12))(1+.^(3)C_(1)x+.^(4)C_(2)x^(2)+ . . .+.^(8)C_(6)x^(6)+ . ..+.^(14)C_(12)x^(12)+ . . .)`
`=.^(14)C_(12)-3xx.^(8)C_(6)+3=.^(14)C_(2)xx.^(8)C_(2)+3`
`=91-84+3=10`