Answer:
We conclude that exists 211680 ways.
Step-by-step explanation:
We know that the three research department is have 10, 7 and 8 members.
We choose a delegate and an alternate to represent the department.
First case: department have 10 members.
So, for a delegate, we have 10 options, and for a alternate 9, so a total of
10 * 9 = 90 options.
Second case: department have 7 members.
So, for a delegate, we have 7 options, and for a alternate 6, so a total of
7* 6 = 42 options.
Third case: department have 8 members.
So, for a delegate, we have 8 options, and for a alternate 7, so a total of
8* 7 = 56 options.
Therefore, we get:
90 · 42 · 56 = 211680
We conclude that exists 211680 ways.
