How many ways are there for 3 males and 3 females to sit if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?
I guess they sit around the table as you mention it in the title of the topic.
So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 3 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 3! different ways, so total 2*3!=12.
Lets first sit the 3 man, 2! ways.
Now since one position is fixed for women, there are 2 women left and they have 2! ways
2! X 2! = 4 answer is diff this way.
or shall we give possibility of 3 ways for women to be fixed with back facing so 3! ways, Lets discuss the doubt.If u like my way of discussion plz give Kudos.
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