Permutation and CombinationHard
Question
In a shooting competition a man can score 0, 2 or 4 points for each shot. Then the number of different ways in which he can score 14 points in 5 shots, is:
Options
A.20
B.24
C.30
D.none
Solution
Find the coefficient of x14 in the expansion of
(x0 + x2 + x4)5 = (1 + x2 + x4)5
=
= (1 - x6)5 (1 - x2)-5
= (1 - 5x6 + 10x12.......) (1 + 5C1x2 + 6C2x4 + 7C3x6 + ....)
= 11C7 - 5 . 8C4 + 10.5
=
+ 50
= 330 - 350 + 50 = 30
(x0 + x2 + x4)5 = (1 + x2 + x4)5
=
= (1 - x6)5 (1 - x2)-5= (1 - 5x6 + 10x12.......) (1 + 5C1x2 + 6C2x4 + 7C3x6 + ....)
= 11C7 - 5 . 8C4 + 10.5
=
+ 50= 330 - 350 + 50 = 30
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