contestada

Each of four friends orders a sweatshirt from a catalog. there are 18 colors of sweatshirts, 6 of which are all cotton and 12 of which are a blend. each one orders a different color (no repeats) at random. what is the probability that the friends order only cotton sweatshirts?
a. 91 divided by 15.
b. 77 divided by 255.
c. 1 divided by 204.
d. 1 divided by 15.

Respuesta :

xoxonikki02
There are 16 sweatshirts in total.
7 of which are cotton. 
There are 4 friends.
Say they all choose cotton sweatshirts,
First friend: (7/16)
Second friend: (6/15)
Third friend: (5/14)
Fourth friend: (4/13)

Multiply these together = (7/16)*(6/15)*(5/14)*(4/13)
= 0.01923076923 = 1.92%

1.92% is the probability all friends order cotton sweatshirts
JeanaShupp

Answer: c. 1 divided by 204.

Step-by-step explanation:

Given: The number of friends = 4

The total number of sweatshirts =18

If each one orders a different color (no repeats) at random., then the total number of ways to order sweatshirts =[tex]^{18}P_4=\frac{18!}{(18-4)!}=\frac{18\times17\times16\times15\times14!}{14!}=73440[/tex]

If the friends order only cotton sweatshirts, then the number of ways to order sweatshirts=[tex]^6P_4=\frac{6!}{(6-4)!}=\frac{6\times5\times4\times3\times2!}{2!}=360[/tex]

Now, the probability that the friends order only cotton sweatshirts =[tex]\frac{360}{73440}=\frac{1}{204}[/tex]

Hence, the probability that the friends order only cotton sweatshirts =[tex]\frac{1}{204}[/tex]

Otras preguntas