The number of terms in the expansion of (a+b+c)^{n} is

  • Option 1)

    \frac{(n+1)\: (n+2)}{2}

  • Option 2)

    n+3

  • Option 3)

    \frac{n(n+1)}{2}

  • Option 4)

    None of these

 

Answers (1)

As learnt in concept

Theorem of Combinations -

The number of combinations of n distinct objects taken r at a time when any object may be repeated any number of times is ^{n+r-1}c_{r}.

- wherein

Coefficient of x^{r} in (1-x)^{-n}.

 

 (a+b+c)^{n}

The general term is _{C_{r}}^{n}a^{x}b^{y}C^{z}

Sum of powers =n

x+y+z=n

Thus no of solutions = ^{n+2}{C_{2}}


Option 1)

\frac{(n+1)\: (n+2)}{2}

This is correct option

Option 2)

n+3

This is incorrect option

Option 3)

\frac{n(n+1)}{2}

This is incorrect option

Option 4)

None of these

This is incorrect option

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