Issam has 11 different CDs, of which 6 are pop music, 3 are jazz and 2 are classical.
Issam makes a selection of 2 pop music CDs, 2 jazz CDs and 1 classical CD. How many different possible selections can be made?
Solution
To find the number of different possible selections, we use combinations to select the CDs from each category.
First, select 2 pop music CDs from 6: \\(_6C_2 = \frac{6!}{2!(6-2)!} = 15\\)
Next, select 2 jazz CDs from 3: \\(_3C_2 = \frac{3!}{2!(3-2)!} = 3\\)
Finally, select 1 classical CD from 2: \\(_2C_1 = \frac{2!}{1!(2-1)!} = 2\\)
Multiply the combinations together to find the total number of selections: \\(15 \times 3 \times 2 = 90\\)
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