How Do You Calculate Different Combinations for Committee Selections?

[SUXinPHY]

Homework Statement

We need to select 5 committee members form a class of 70 students.

• How many possible samples exists?
• How many possible samples exists if the committee members all have different roles?

Homework Equations

_nC_r = n! / (r!(n-r)!)

The Attempt at a Solution

I am able to solve the first part.
"How many possible samples exists?" = ₇₀C₅

But I am unsure of the second.
Would it simply be:
₇₀C₁ x ₆₉C₁ x ₆₈C₁ x ₆₇C₁ x ₆₆C₁ x ₆₅C₁

 

[jz92wjaz]

Second part is very close. I think you understand it but made a mistake when writing it down.

 

[SUXinPHY]

Second part is very close. I think you understand it but made a mistake when writing it down.

My mistake, 65C1 should not be there.