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Consider the expansion of (a+b+c+d)^(6)....

Consider the expansion of `(a+b+c+d)^(6)`. Then the sum of all the coefficients of the term
Which contains both a and b is

A

4096

B

1560

C

3367

D

670

Text Solution

Verified by Experts

The correct Answer is:
B
We have `(a+b+c+d)^(6)`
Sum of coefficient which contains all of a,b,c and d
= Number of ways of distributing six distinct objects in fourt boxes such that no box remains empty
`= 4^(6) - .^(4)C_(1)3^(6) +.^(4)C_(1) - .^(4)C_(1)1^(6) = 1560`
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CENGAGE PUBLICATION-BINOMIAL THEOREM-Linked Comphrension
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  6. If the 2nd, 3rd and 4th terms in the expansion of (x+a)^n are 240, 7...

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  7. An equation a(0) + a(2)x^(2) + "……" + a(99)x^(99) + x^(100) = 0 has ro...

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  10. If a= .^(20)C(0) + .^(20)C(3) + .^(20)C(6) + .^(20)C(9) + "…..", b = ....

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  11. If a= ^(20)C(0) + ^(20)C(3) + ^(20)C(6) + ^(20)C(9) + "…..", b = ^(20)...

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  16. Let P =sum(r=1)^(50)(""^(50+r)C(r)(2r-1))/(""^(50)C(r)(50+r)), R = su...

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  17. Let Q = sum(r=0)^(50)(""^(50)C(r))^(2), R = sum(r=0)^(100)(-1)^(r) (""...

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  18. If (1+x-2x^(2))^(6) = 1 + a(1)x+a(2)x^(2) + "……" + a(12)x^(12), then f...

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