Problem of the Day


Four families of three are lining up for a photo. How many ways can they line up if all of the members in each family must stand together?

A. 12
B. 4!3!
C. 7!
D. 4!6^4
E. 12!

Reveal Answer

Answer

[latexpage]

D. $4!6^4$

See the Solution

Solution

[latexpage]

First calculate the number of ways to arrange the four families: $4!=24$. Then, note that each family can be rearranged 3! ways. For each of the 24 ways we can arrange the families, the members within the families can be arranged $3!3!3!3!=6^4$ ways. Hence, there are $4!6^4$ ways to arrange the people.


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