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In how many ways can three identical emeralds, two identical diamonds, and two different opals be arranged in a row in a display case?*

Sagot :

Urbanbernabethidn

Answer:

7!/(3!*2!) = 7*5*4*3 = 420 ways

Jerlestan61idn

Answer:

They can be arranged in 210 ways.

We have given that, 3 identical emeralds 2 identical diamonds and 2 different opals

What is the arrangement of n object  where n₁ is one kind, n₂ is a second kind, and n₃ is a third kind?

The arrangement of n objects where n₁ is one kind, n₂ is a second kind, and n₃ is a third kind is given by

The total number of gems =7

3 of the first kind, 2 of the second kind and 2 of the third kind

Therefore, we get

Therefore ,they can be arranged in 210 ways.

Hope it helps po

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