JEE PYQ: Permutation And Combination Question 38
Question 38 - 2019 (12 Apr Shift 1)
The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct is:
(1) $2^{20} - 1$
(2) $2^{21}$
(3) $2^{20}$
(4) $2^{20} + 1$
Show Answer
Answer: (3)
Solution
Choose $r$ identical objects ($0 \leq r \leq 10$) and $10 - r$ distinct objects. $= \sum_{r=0}^{10} {}^{21}C_{10-r} = {}^{21}C_{10} + {}^{21}C_9 + \cdots + {}^{21}C_0 = \frac{2^{21}}{2} = 2^{20}$.
BETA
