Answered

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Five couples want to have their pictures taken. In how many ways can they arrange themselves in a row if a. couples must stay together? b. they may stand anywhere?

Sagot :

Alphabetagammaidn
a. Couples must stay together

Since there are five couples, there are 10 people altogether. But if couples must stay together, then, we can count each couple as one. So, the number of ways they can be in a row is 5! (5 factorial, which is equal to 120). But, in each couple, there are 2! (2 factorial, which is equal to 2) ways that they can also be arranged. If we multiply 2! ways in each couple, that would be 2x5, which is equal to 10. So if we multiply 120 by 10, the answer would be 1200.

Therefore, there are 1200 ways.

b. They may stand anywhere

Since there are 10 people altogether, and they may stand anywhere, the number of ways they can be arranged in a row is simply 10! (10 factorial), which is equal to 3,628,800.

Therefore, there are 3,628,800 ways.
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