A test consists of 6 multiple choice questions,

Question:

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____________.

Solution:

Select any 4 correct questions in ${ }^{6} C_{4}$ ways.

Number of ways of answering wrong question $=3$

$\therefore$ Required number of ways $={ }^{6} C_{4}(1)^{4} \times 3^{2}=135$.

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