CA Foundation · Quantitative Aptitude · Permutations and Combinations
Which expression equals 10C3 written using factorials?
10C3 equals 10! divided by (3! × 7!), which is 120. The formula nCr = n!/(r!(n−r)!) applies with n−r = 7. The option 10!/7! is 10P3 = 720 because it leaves out division by 3!.
- A10! ÷ (3! × 6!)
- B10! ÷ (3! × 7!)Correct
- C10! ÷ 7!
- D10! ÷ (3! × 10!)
Explanation
nCr = n!/(r!(n−r)!). With n = 10 and r = 3, this is 10!/(3! × 7!) = 120. The option 10!/7! equals 10P3 = 720, which omits dividing by 3!, and the first option uses 6! instead of 7!.
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