A bag contains 25 white marbles and 32 black marbles. The probability P(X) of selecting without replacement a sample of size 9 of 3 white marbles and 6 black marbles is
A) ${ } _ { 57 } \mathrm { C } _ { 9 }$
B) ${ } _ { 57 } \mathrm { C } _ { 9 } / \left\{ { } _ { 3 } \mathrm { C } _ { 25 } \times { } _ { 6 } \mathrm { C } _ { 32 } \right\}$
C) $\left\{ { } _ { 6 } \mathrm { C } _ { 3 } \times { } _ { 32 } \mathrm { C } _ { 25 } \right\} / { } _ { 57 } \mathrm { C } _ { 9 }$
D) $\left\{ { } _ { 3 } \mathrm { C } _ { 25 } \times { } _ { 6 } \mathrm { C } _ { 32 } \right\} / { } _ { 57 } \mathrm { C } _ { 9 }$

Question

A bag contains 25 white marbles and 32 black marbles. The probability P(X) of selecting without replacement a sample of size 9 of 3 white marbles and 6 black marbles is 
A) ${ } _ { 57 } \mathrm { C } _ { 9 }$
B) ${ } _ { 57 } \mathrm { C } _ { 9 } / \left\{ { } _ { 3 } \mathrm { C } _ { 25 } \times { } _ { 6 } \mathrm { C } _ { 32 } \right\}$
C) $\left\{ { } _ { 6 } \mathrm { C } _ { 3 } \times { } _ { 32 } \mathrm { C } _ { 25 } \right\} / { } _ { 57 } \mathrm { C } _ { 9 }$
D) $\left\{ { } _ { 3 } \mathrm { C } _ { 25 } \times { } _ { 6 } \mathrm { C } _ { 32 } \right\} / { } _ { 57 } \mathrm { C } _ { 9 }$

Quizplus · Accepted Answer

The probability of selecting 3 white and 6 black marbles is the number of ways to choose 3 white marbles from 25 and 6 black marbles from 32, divided by the total number of ways to choose 9 marbles from 57.

A Bag Contains 25 White Marbles and 32 Black Marbles 57C9{ } _ { 57 } \mathrm { C } _ { 9 }57​C9​

A Bag Contains 25 White Marbles and 32 Black Marbles ${ } _ { 57 } \mathrm { C } _ { 9 }$