Question

The number of terms in the expansion of (2x + 3y − 5z)

8 is
(a) C(10, 8) (b) C(11, 8) (c) C(10, 3)​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The number of terms in the expansion of

$\sf{ {(2x + 3y - 5z)}^{8} }$ is

(a) C(10, 8)

(b) C(11, 8)

(c) C(10, 3)

EVALUATION

We know that the number of terms in the expansion of

$\sf{ {(x_1 + x_2 + ... + x_r)}^{n} }$ is

$\sf{ {}^{n + r - 1}C_{r - 1} }$

Here the given expansion is

$\sf{ {(2x + 3y - 5z)}^{8} }$

So r = 3 & n = 8

Hence the number of terms

$\sf{ = {}^{8 + 3- 1}C_{3 - 1} }$

$\sf{ = {}^{10}C_{2} }$

$\sf{ = {}^{10}C_{10 - 2} \: \: \bigg( \because \: \:{}^{n}C_{r} = {}^{n}C_{n - r} \: \bigg) }$

$\sf{ = {}^{10}C_{8} }$

$\sf{ =C(10,8) }$

FINAL ANSWER

Hence the correct option is (a) C(10, 8)

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