Three research department is have 10 seven and eight members respectively each department is to select a delicate in an alternate to represent the department at a conference in how many ways can this be done

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.