Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationnPr & nCrMedium2 minQB

MathematicsMediumsingle choice

The number of ways of choosing n objects out of $3 n + 1$ objects of which 'n' are identical and $(2 n + 1)$ are distinct is

Answer:

Solution:

If we choose $k (0 \leq k \leq n)$ identical objects, then we must choose $n - k$ distiact objects.

This can be done in $^{2 n + 1} C_{n - k}$ ways.

Thus the required number of ways

$= \sum_{k = 0}^{n}^{2 n + 1} C_{n - k} = 2^{2 n}$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:nPr & nCr

⏱ 2mℹ️ Source: QB

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