Determine the no. of terms in the expansion of ( a + b + c + d ) 5 and ( 1 + a + a 2 + a 3 ) 5 Options: A . &nbsp56, 16 B . &nbsp32, 24 C . &nbsp165, 32 D . &nbsp32, 32 E . &nbsp5, 4

Determine the no. of terms in the expansion of (a+b+c+d)5 and (1+a+a2+a3)5

Question

Determine the no. of terms in the expansion of

(a + b + c + d)^{5}

and

(1 + a + a^{2} + a^{3})^{5}

Answer: Option A
:
A
No. of terms in expansion of

(a + b + c + d)^{5}

= Number of solution of (a + b + c + d) = 5,

^{8} C_{3}

= 56
No. of terms in expansion of

(1 + a + a^{2} + a^{3})^{5} = (5 \times 3) + 1 = 16

Hence option (a)

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