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Permutation and Combination question bank (Quantitative Aptitude)

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Q1.

In how many ways can $n$ books be arranged in a row so that two specified books are not together?

(A)
$n! - (n - 2)!$
(B)
$(n - 1)! (n - 2)$
(C)
$n! - 2(n - 1)!$
(D)
$(n - 2) n!$
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Q2.

In how many ways can $5$ boys and $3$ girls sit in a row so that no two girls are together?

(A)
$5! \times 3!$
(B)
$^4P_3 \times 5!$
(C)
$^6P_3 \times 5!$
(D)
$^5P_3 \times 3!$
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