Use the Combinations Formula
Use the formula for
$$\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } }$$ to evaluate the expression.
-${ } _ { 4 } \mathrm { C } _ { 0 }$
A) 1
B) 40
C) 0
D) 24

Question

Use the Combinations Formula
Use the formula for
 $$\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } }$$ to evaluate the expression.
-${ } _ { 4 } \mathrm { C } _ { 0 }$
A) 1
B) 40
C) 0
D) 24

Quizplus · Accepted Answer

The Combinations Formula is given by $$\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } } = \frac{n!}{r!(n-r)!}$$
where n is the total number of objects and r is the number of objects we are choosing.

For this problem, we have $$\mathrm {4} ^ { \mathrm {C} _ { \mathrm {0} } }$$
So n = 4 and r = 0. Plugging this into the formula, we get

$$\begin{aligned} \mathrm {4} ^ { \mathrm {C} _ { \mathrm {0} } } &= \frac{4!}{0!(4-0)!} \
&= \frac{24}{1 \cdot 24} \
&= 1 \end{aligned}$$

Therefore, the answer is A) 1.

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

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