JEE MAIN - Mathematics (2003 - No. 41)
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
$$7!\, \times 5!\,\,$$
$$6!\, \times 5!$$
$$30!$$
$$5!\, \times 4!$$
Explanation
6 men can sit at the round table = $$\left( {6 - 1} \right)! = 5!$$ ways
Now at the round table among 6 men there are 6 empty places and 5 women can sit at those 6 empty positions.
So total no of ways 6 men and 5 women can dine at the round table
= $$5!\, \times {}^6{C_5} \times 5!$$
= $$5!\, \times 6 \times 5!$$
= $$5!\, \times 6!$$
Comments (0)
