JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of ways of choosing \(10\) objects out of \(31\) objects of which \(10\) are identical and the remaining \(21\) are distinct, is
- A \(2^{20}\)
- B \(2^{20}+1\)
- C \(2^{21}\)
- D \(2^{20}-1\)
Answer & Solution
Correct Answer
(A) \(2^{20}\)
Step-by-step Solution
Detailed explanation
Since \(^{21}{C_0} + .....{ + ^{21}}{C_{10}}{ + ^{21}}{C_{11}} + .....{ + ^{21}}{C_{21}} = {2^{21}}\) \( \Rightarrow \) but we have to select \(10\) objects and \(^{21}{C_0} + .....{ + ^{21}}{C_{10}}{ + ^{21}}{C_{11}} + .....{ + ^{21}}{C_{21}}\)…
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