JEE Main 2019MathematicsPermutation CombinationMediumMCQ

JEE Main 2019 — Permutation Combination Question with Solution

JEE Main 2019 (12 Apr Shift 1)

Question

The Number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is:

Choose an option

Show full solutionCorrect option: A
Correct answer
A220

Step-by-step explanation

There is only one way in which we can choose one, two or more objects from 10 identical objects.
Number of ways of selecting 10 objects
= 21C10+ 21C9+ 21C8+ 21C7+ 21C6+ 21C5+ 21C4+ 21C3+ 21C2+ 21C1+ 21C0
 We know  nCr= nCn-r and
⇒221= 21C0+ 21C1+ 21C2+ 21C3+ 21C4+.........+ 21C21            ∵ 21C21= 21C0 21C20= 21C1 21C19= 21C2 
=2 21C0 + 21C1 + 21C2 +……………+ 21C10
⇒ 21C0+ 21C1 +21C2 +.........+ 21C10 = 220

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About this question

This is a previous-year question from JEE Main 2019, covering the Permutation Combination chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.