A test consists of 6 multiple choice questions, each having 4 alternative ans wers of which&nbs

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6.Permutation and Combination

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A test consists of $6$ multiple choice questions, each having $4$ alternative ans wers 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

A

$135$

B

$140$

C

$125$

D

$130$

(JEE MAIN-2020)

Solution

$Ways ={ }^{6} C _{4} \cdot 1^{4} \cdot 3^{2} $

$=15 \times 9 $

$=135 $

Standard 11

Mathematics

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