Use the Combinations Formula
Use the formula for
$$\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } }$$ to evaluate the expression.
-In a student government election, 5 seniors, 3 juniors, and 2 sophomores are running for election. Students elect four at-large senators. In how many ways can this be done?
A)210
B)5040
C)151,200
D)30

Question

Use the Combinations Formula
Use the formula for
 $$\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } }$$ to evaluate the expression.
-In a student government election, 5 seniors, 3 juniors, and 2 sophomores are running for election. Students elect four at-large senators. In how many ways can this be done?
A)210
B)5040
C)151,200
D)30

Quizplus · Accepted Answer

The total number of candidates is $5 + 3 + 2 = 10$. To find the number of ways to elect 4 senators from these 10 candidates, we use the combination formula $\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } } = \frac{n!}{r!(n-r)!}$, where $n = 10$ and $r = 4$. Thus, the calculation is $\frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210$.

Use the Combinations Formula Use the Formula For nCr\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } }nCr​

Use the Combinations Formula
Use the Formula For $\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } }$