Use the Combinations Formula
Use the formula for
$$\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } }$$ to evaluate the expression.
-A stack of 10 different cards are shuffled and spread out face down. If 4 cards are turned face up, how many different 4-card combinations are possible?
A)210
B)5040
C)151,200
D)2520

Question

Use the Combinations Formula
Use the formula for
 $$\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } }$$ to evaluate the expression.
-A stack of 10 different cards are shuffled and spread out face down. If 4 cards are turned face up, how many different 4-card combinations are possible?
A)210
B)5040
C)151,200
D)2520

Quizplus · Accepted Answer

The formula for combinations is $\mathrm { n } ^ { \mathrm { C } _ { \mathrm { r } } } = \frac{n!}{r!(n-r)!}$. Here, $n=10$ and $r=4$, so the number of combinations is $\frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210$. This represents the number of different 4-card combinations possible from a stack of 10 different cards.

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

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