A jar contains 6 chocolate chip cookies and 9 peanut butter cookies. Richard grabs 3 cookies at random to pack in his lunch. What is the probability that he dre
Mathematics
andrewace
Question
A jar contains 6 chocolate chip cookies and 9 peanut butter cookies. Richard grabs 3 cookies at random to pack in his lunch. What is the probability that he drew 2 chocolate chip cookies and 1 peanut butter cookie?
A. [tex] \frac{1}{54}[/tex]
B. [tex]\frac{1}{27} }[/tex]
C. [tex]\frac{9}{91} }[/tex]
D. [tex]\frac{27}{91} }[/tex]
A. [tex] \frac{1}{54}[/tex]
B. [tex]\frac{1}{27} }[/tex]
C. [tex]\frac{9}{91} }[/tex]
D. [tex]\frac{27}{91} }[/tex]
2 Answer

1. User Answers Anonym
Here, Your Answer would be 9/91
In short, Answer is Option C
Hope this helps! 
2. User Answers JeanaShupp
Answer: D. [tex]\dfrac{27}{91}[/tex]
Stepbystep explanation:
Given: Number of chocolate chip cookies  6
Number of peanut butter cookie = 9
Total cookies = 6+9=15
The total number of combinations of selecting 3 cookies from 15 cookies
[tex]^{15}C_3=\dfrac{15!}{(153)!3!}=455[/tex]
The number of combinations to select 2 chocolate chip cookie=
[tex]^{6}C_2\dfrac{6!}{(62)!2!}=15[/tex]
The number of combinations to select 1 peanut butter cookie=
[tex]^{9}C_1=\dfrac{9!}{(91)!1!}=9[/tex]
The probability that he drew 2 chocolate chip cookies and 1 peanut butter cookie=[tex]\dfrac{^{9}C_1\times ^{9}C_1}{^{15}C_3}=\dfrac{15\times9}{455}=\dfrac{27}{91}[/tex]