Question

What is the value of the coefficient of the 4th term in the expansion of (a + b)^12?A. 220B. 985C. 1320D. 445

Answer 1

Binomial expansion

`(a+b)^n=\sum ^n_(k=0)nC_k\cdot a^(n-k)\cdot b^k`

The coefficient of each term is:

`_nC_k`

That is, the number of combinations of k objects from a set with n objects

In the binomial:

`(a+b)^(12)`

the value of n is n = 12. In the fourth term, k = 3 (remember that k starts at zero). Therefore, the coefficient of the 4th term is:

`_(12)C_3=(12!)/((12-3)!\cdot3!)=(12!)/(9!\cdot3!)=(12\cdot11\cdot10\cdot9!)/(9!\cdot3\cdot2\cdot1)=(1320)/(6)=220`