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
Create a free account to view solution
View Solution FreeMore Permutation and Combination Questions
In a unique hockey series between India & Pakisthan, they decide to play on till a team wins 5 matches. The number of wa...In a unique hockey series between India & Pakistan, they decide to play on till a team wins 5 matches. The number of way...In a plane there are 10 points out of which 4 are collinear, then the number of triangles that can be formed by joining ...There are 10 students in a class in which three A, B, C are girls. The number of ways to arrange them in a row when any ...The three sides AB, BC and CA of any ᐃABC are having 3, 4, and 5 internal points respectively. Then the number of ...