Question

Determine the no. of terms in the expansion of (a + b + c + d)${}^5$ and (1 + a + a${}^2$ + a${}^3$)${}^5$

• A. 56, 16
• B. 32, 24
• C. 165, 32
• D. 32, 32
• E. 16, 14

Answer 1

The correct option is A 56, 16

Soln: 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*3) + 1 = 16

Hence option (a)