Question

3 ladies and 3 gents can be seated at a round table so that any two and only two of the
ladies sit together. The number of ways is
(b) 27
(c) 72
(d) none of these
The number of ways in which the letters of the word DOGMATIC' can be arranged is
d) none of these​

Answer 1

Answer:

72 possible ways

Step-by-step explanation:

How many ways can 3 ladies and 3 gents can be seated around a round table so that any two and only two ladies sit together?

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We have 3 ladies and 3 gents.

Constraint : any two and only two ladies sit together.

We can get any two ladies out of 3 ladies in 3C2 ways, 3 ways.

Only two ladies sit together means remaining lady can’t sit adjacent to selected ladies(in previous step), which leaves us with the option that selected ladies are surrounded by gents.

selected two ladies can sit in 2! ways.

now 4 seats remains and remaining lady can’t took the adjacent one, which leaves 2 possible ways for her.

Gents can be arranged in 3! ways on the remaining seats.

So total combination would be : (3C2)*(2!)*(2)*(3!) = 72 possible ways.