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A small community college in Ohio has four student organizations (A, B, C, and D). Organization A has 5 students, B has 8, C has 10, and D has 12. It is thought that new students have no preference for one of these organizations over the other. If seven new students are admitted to the college, what is the probability that one student will choose organization A, one will choose B, two will choose C, and three will choose D?

Respuesta :

Answer: Our required probability is 0.058.

Step-by-step explanation:

Since we have given that

Number of students in A = 5

Number of students in B = 8

Number of students in C = 10

Number of students in D = 12

Total number of students in all = 5 + 8 + 10 + 12 = 35

So, we need to find the probability that one student will choose  A , 1 student will choose  B, 2 will choose C and 3 will choose D.

So, it becomes,

[tex]\dfrac{^5C_1\times ^8C_1\times ^{10}C_2\times ^{12}C_3}{^{35}C_7}\\\\=\dfrac{5\times 8\times 45\times 220}{6724520}\\\\=\dfrac{396000}{6724520}\\\\=0.058[/tex]

Hence, our required probability is 0.058.

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