Question
Question: Out of 5 apples, 10 mangoes and 15 oranges, any 15 fruits distributed among two persons. The total n...
Out of 5 apples, 10 mangoes and 15 oranges, any 15 fruits distributed among two persons. The total number of ways of distribution
A
66
B
36
C
60
D
None of these
Answer
66
Explanation
Solution
Number of ways = coefficient of x15 in the expansion (1 + x + x2 + x3 + x4 + x5)
(1 + x + x2 + .......+x10)
(1 + x + x2 + ........+ x15)
(1 + x + x2 + x3 + x4 + x5) (1 + x + x2 + .........+x10)
(1 + x + x2 + .........+ x15)
= (1 – x6 – x11) (1 + 3C1x + 4C2x2 + ........+ 6+C4 + 11C9x9+ 17C15x15 + ..............)
= .....+...............+ x15 (- 11C9 – 6C4 + 17C15)
= .......... + ......+ x15 (-55 – 15 + 136) = x15 x 66
∴ Coefficient of x15 = 66.