JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Permutations and Combinations

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A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is

Answer: 135

Solution

The four questions to be answered correctly can be chosen in

(4 6) = 15

ways, and each of those four has just one correct response. Each of the remaining two questions must be answered wrongly, which can happen in

3

ways apiece, giving

3^{2} = 9

ways. The total number of ways is

15 \times 9 = 135

JEE Main · 2020 · 04 Sep 2020 · Shift 2 · Integer answer

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