3 men and 3 women are sit at a round table in how many ways can they sit that no two women sit together
Answers
72 Ways is number of seating arrangements for 3 men and 3 women to sit around a table so that exactly two women are together
Step-by-step explanation:
Let say Position 1 & 2 is taken by two Women
then these two women can be selected in ³C₂ = 3 Ways
and can be arranged in 2! (we can also say ³P₂ = 6)
=> 3 * 2 = 6 Ways
Now position 3 & 6 has to be taken by Men as exactly two women are together.
Hence 3 & 6 Position can be taken by Men in ³C₂ * 2! = 6 Ways
(we can also say ³P₂ = 6)
Now we remain with two positions 4 & 5
& two person one man & one woman
who can be sitted in 2 Ways
Hence the number of seating arrangements for 3 men and 3 women to sit around a table so that exactly two women are together = 6 * 6 * 2
= 72 Ways
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