Haryana Police Constable Model Paper 1

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Question : 88 of 100

Marks: +1, -0

What is the number of terms in the expansion of

(\a + \b + \c)^ \n, \n ∈ \N?

$\n + 1$
$\n + 2$
$\n(\n + 1)$
${(\n+1)(\n+2)}/2$

Solution:

Concept:
The total number of terms in the expansion of

(\a_{1} + \a_{2} + … + \a_{\k})\n

is given by

^{\n + \k -1 }\C _{ \k -1}

^{\n}\C_{\r}=\n!/{(\n−\r)!\r!}

\n!=\n(\n−1) .... 2×1

Calculation:

(\a + \b + \c)^\n

Here,

\n = \n \and \k = 3

So, total number of terms =

^{\n+3-1}\C_{3-1}

= ^{{\n + 2}}\C_{2}

= {(\n+1)(\n+2)}/2

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