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?
D. $4!6^4$See the Solution
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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