Question

1.A three-course meal at a restaurant consists of a choice of one of 5 salads, one of 7 entrees and one of 4 desserts. If a diner chooses each course of her meal randomly, what is the probability that she will choose: a Cobb salad, grilled ribs with corn on the cob, and a slice of boysenberry cobbler.

2. If the letters ACDEINOTU are arranged in order randomly, what is the probability that the arrangement will spell the word "EDUCATION"

3. A phone number(not counting the area code) consists of a sequence of seven digits from 0-9. What is the probability of randomly generating seven digits and getting the phone number of one of the 25 students in a Statistics class ( assume each student has exactly one phone number)

Answer 1

1) total number of arrangement of dinner =5*7*4=140

hence probability that she will choose: a Cobb salad, grilled ribs with corn on the cob, and a slice of boysenberry cobbler =1/140

2)

there are 1 A ; 1 C ; 1 D ; 1 E ; 1 I ; 1N ; 1 O ; 1 T and 1 U in total 9 letters.

total number of arangements =9! =362880

therefore probability that the arrangement will spell the word "EDUCATION" =1/362880

3)

totalnumber of possible sequnce =10⁷ =10000000

hence probability =25/10000000 =1/400000