Question

six couples want to have their picture taken. in how many ways can they arrange themselves in a row?​

Answer 1

Answer: Five couples in a row can be arranged in (5!) = 120 ways. In every such arrangement, positions of husband and wife of each couple can be chosen in (2!) = 2 ways. So, for five couples positions of husbands and wives can be = (2 * 2 * 2 * 2 * 2) = (2^5) = 32

Step-by-step explanation:

Answer 2

Answer:

46080

Step-by-step explanation:

Assumption: No two person from different couples can take picture together.

No. of ways in which N things can be arranged in a row is given by N!

This implies that, no. of the way in which 6 couples(n=6 ;considering 2 of them as 1 unit) can arrange in a row is 6! = 720.

Also note that couple can change there position in 2 ways, since there are 6 couple so interchanging of respective position by couples can be possible in $2^6 = 64$ ways.

Finally total no of ways in which six couples can arrange themselves in a row is 64*720 = 46080 ways.