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Question

Mathematics Question on Multiplication Theorem on Probability

Four men and three women are standing in a line for railway ticket. The probability of standing them in alternate manner is

A

135\frac{1}{35}

B

133\frac{1}{33}

C

184\frac{1}{84}

D

17\frac{1}{7}

Answer

135\frac{1}{35}

Explanation

Solution

∵\because Total outcomes =7P7=7!={ }^{7} P_{7}=7 !
and favourable outcomes =3!×4!=3 ! \times 4 !
∴\therefore Required probability = Favourable outcomes  Total outcomes =\frac{\text { Favourable outcomes }}{\text { Total outcomes }}
=3!×4!7!=3×2×1×4!7×6×5×4!=135=\frac{3 ! \times 4 !}{7 !}=\frac{3 \times 2 \times 1 \times 4 !}{7 \times 6 \times 5 \times 4 !}=\frac{1}{35}