Respuesta :
Answer:
There are 455 different handfuls of 12 jellybeans possible
Step-by-step explanation:
From the given information;
we are told that there exist 50 kinds of jellybean for each of these colors (red, orange, green, yellow)
Also the jellybeans of each color are identical.
i.e Let say y represent the color of the jellybean.
Then y₁ = y₂ = y₃ = y₄ corresponds to each of these colors (red, orange, green, yellow)
The objective is to determine how many different handfuls of 12 jellybeans are possible?
So;
y₁ + y₂ + y₃ + y₄ = 12
Therefore; the number of different handfuls of 12 jellybean possible can be computed by using the formula:
[tex]C(r+k-1,r) = \dfrac{(r+k-1)!}{r! (k-1)!}[/tex]
where;
r =12 jellybeans
k = 4 types of colors
[tex]C(12+4-1,4) = \dfrac{(12+4-1)!}{12! (4-1)!}[/tex]
[tex]C(15,4) = \dfrac{15!}{12! (3)!}[/tex]
[tex]C(15,4) = \dfrac{15\times 14 \times 13 \times 12!}{12! (3)!}[/tex]
[tex]C(15,4) = \dfrac{15\times 14 \times 13 }{3!}[/tex]
[tex]C(15,4) = \dfrac{15\times 14 \times 13 }{3 \times 2 \times 1}[/tex]
[tex]C(15,4) =5\times 7 \times 13[/tex]
[tex]C(15,4) =455[/tex]
There are 455 different handfuls of 12 jellybeans possible
There are [tex]455[/tex] different handfuls of [tex]12[/tex] jellybeans that are possible.
Probability:
Probability is termed as the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen. The probability formula is determined as the possibility of an event to happen is equal to the ratio of the number of outcomes and the total number of outcomes.
Given information are:
There are exist of [tex]50[/tex] kinds of jellybean of different colors i.e. red, orange, green, yellow.
The jellybeans of each color are identical.
i.e Let say [tex]y[/tex] represent the color of the jellybean.
Then [tex]y_1=y_2=y_3=y_4[/tex] corresponds to each of these colors (red, orange, green, yellow)
So,
[tex]y_1+y_2+y_3+y_4=12[/tex]
Therefore, the number of different handfuls of [tex]12[/tex] jellybean possible can be computed by using the formula:
[tex]C\left ( r+k-1,r \right )=\frac{\left (r+k-1 \right )!}{r!\left ( k-1 \right )!}[/tex]
where,
[tex]r=12[/tex] jellybeans
[tex]k=4[/tex] types of colors
[tex]C\left ( 12+4-1,4 \right )=\frac{\left (12+4-1 \right )!}{12!\left ( 4-1 \right )!} \\ C(15,4)=\frac{15!}{12!(3)!} \\ C\left ( 15,4 \right )=\frac{15\times 14\times 13\times 12!}{12!(3!)} \\ C(15,4)=\frac{15\times 14\times 13}{3!} \\ C(15,4)=\frac{15\times 14\times 13}{3\times2\times1} \\ C(15,4)=5\times7\times13 \\ C(15,4)=455[/tex]
So, the possibility are [tex]455[/tex] different handfuls of [tex]12[/tex] jellybeans.
Learn more about the topic Probability: https://brainly.com/question/26571971
