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Asked by coolestoginthehood | 30 Dec, 2023, 08:00: PM
Expert Answer
Now, (1+x)10 = 10C0 + 10C1 x + 10C2 x2 +...
(1+x)15 = 15C0 + 15C1 x + 15C2 x2 + ...
Multiplying the above expansions, we get
(1+x)10 (1+x)15 = 10C0 15C0 + (10C0 15C1 + 10C1 15C0)x + ...
Coefficient of xn in this case is 10C0 15Cn + 10C1 15Cn-1 + 10C2 15Cn-2 + ... + 10Cn 15C0
The expression 10C0 15C14 + 10C1 15C13 + 10C2 15C12 + ... + 10C10 15C4
represents the coeffcient of x14
Now, coeff. of x14 in the expansion of (1+x)25 is 25C14 i.e. 25C11
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