Question

4. How many ways can you choose three toppings from 10 different toppings available at a Pizza delivery store? Also if you are ranking the three toppings chosen out of 10 toppings, how many different ways are possible? 5. If 40 % of all commuters ride to work in carpools, find the probability that exactly 4 will ride in carpools out of 10 workers? Also find the probability that nobody will ride in carpools out of 10 workers? 6. If 80 % of the applicants are able to pass a driver's proficiency road test, find the average number of applicants who will pass out of 5 applicants. Also find the probability that all 5 applicants will pass the road test. I

Answer 1

4. We need to choose 3 toppings of pizza out of 10.

Thus, the number of ways are ¹⁰C₃ = 120 ways.

When you rank these 3 toppings out of 10. Then we are using permutations. Since, order matters.

Thus, the number of ways are ¹⁰P₃ = 720 ways.

5. Let n = 10 , p = 0.4

Using P(x = r)=$\binom{n}{r}$ p^r (1-p)^{n- r}

P( x = 4) = $\binom{10}{4}$ (0.4)⁴ (0.6)⁶

= 210(0.0256)(0.0467)

= 0.2510

P( x = 0) = $\binom{10}{0}$ (0.4)⁰ (0.6)¹⁰

= 1*1*0.006

= 0.006

C. n = 5 , p = 0.8

Average applicants = np

= 5(0.8)

= 4

Thus, 4 applicants.

P ( all 5 pass the test) = (0.8)⁵

= 0.3277

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