Q. 105.0( 1 Vote )

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Answer :

Given: there are m men and n women where m>n

To find: out their possible way of sitting arrangements in a row such that no two women sit together

Let m = 2 then possible arrangement is

_ m _ m _

Here 3(2 + 1) gaps for women can by made by 2 men so that no two of them comes together

When m men are there, m seats can be occupied by men and m + 1 seat can by women

Formula used:

Number of arrangements of n things taken all at a time = P(n, n) Total number of arrangements of men

= the number of arrangements of m things taken all at a time

= P(m, m)  { 0! = 1}

= m!

Formula used:

Number of arrangements of n things taken r at a time = P(n, r) Total number of arrangements of women

= the number of arrangements of m + 1 things taken n at a time

= P(m + 1, n)  Hence, total possible arrangements of m men and n women in a row such that no two women come together  Hence, Proved.

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