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 no of ways is​

Answer 1

in 72 Ways , 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together.

Step-by-step explanation:

Possible arrangements :

2 Ladies sitting together can be selected in  ³P₂  = 6 Ways

now remaining 1 Lady can not sit adjacent to these ladies

so out of remaining 4 seats she can sit only on two seats

hence  ²P₁  = 2 Ways

so Ladies can sit in  6 * 2 = 12  Ways

for Three Gents  3 Seats are Left so gents can sit in ³P₃  = 6 Ways

Total Number of Ways = 12 * 6 = 72

3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together in 72 Ways

Similar Questions :

Five persons wearing badges with numbers 1,2,3,4,5 are seated on 5 chairs around a circular table.    

https://brainly.in/question/11759574

https://brainly.in/question/11763105

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

https://brainly.in/question/9477524

Answer 2

Step-by-step explanation:

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.