Mathematics

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]

2 Answer

  • Here, Your Answer would be 9/91

    In short, Answer is Option C

    Hope this helps!
  • Answer: D. [tex]\dfrac{27}{91}[/tex]

    Step-by-step 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!}{(15-3)!3!}=455[/tex]

    The number of combinations to select 2 chocolate chip cookie=

    [tex]^{6}C_2\dfrac{6!}{(6-2)!2!}=15[/tex]

    The number of combinations to select 1 peanut butter cookie=

    [tex]^{9}C_1=\dfrac{9!}{(9-1)!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]

NEWS TODAY