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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) 729 (b) 3367 (c) 2702 (d) 1024

A

2884

B

4032

C

1974

D

2702

Text Solution

Verified by Experts

The correct Answer is:
D
Sum of coefficient which contains both a and b.
= Number of ways of distributing six distinct objects in four boxes (a,b,c,d)
- Number of ways of distributing six distinct objects in the three boxes (a,c,d)
- Number of ways of distributing six distinct objects in three boxes `(b,c,d)`
+ Number of ways of distributing six distinct objects in two boxes (c,d)
`= 4^(6) - 2 xx3^(6) + .^(2)C_(20 xx 2^(6) = 2702`
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