For each problem, set up but DO NOT SIMPLIFY OR REDU answers. All questions are

Question

For each problem, set up but DO NOT SIMPLIFY OR REDU answers. All questions are 2 points each. If you have any Baskin Robbins has 2 types of sizes, 31 flavors, and 6 toppings. How many different ways are possible if you choose one from each category? How many different 3-digit combinations are possible if the last digit must be odd and no repetition is allowed? A bag contains 17 marbles: 10 purple and 7 green. the green ones are numbered 11 through 17. If one marble is chosen, what is the probability that it is purple? If one marble is chosen, what is the probability that it is green?

Explanation / Answer

2.

3 digit number set in which the last digit is odd (Without repetition)

for A we have total choices = 1,2,3,4,5,6,7,8,9 , not zero otherwise the number will be two digit number

for B = 0,1,2,3,4,5,6,7,8,9

for C = 1,3,5,7,9 (odd)

without repetition,

so total number of ways (we'll do this by cases) = (choose C)(choose A)(B=0) + (choose A)(choose B)(C=1) +(choose A)(choose B)(C=3)+(choose A)(choose B)(C=5)+(choose A)(choose B)(C=7)+(choose A)(choose B)(C=9)

{In last four cases we didn't include the case when b=0 because we made all possible combination of b=0 in first case}

1.

(choose C)(choose A)(B=0) = when {c =1,+,c =3,+,c =5,+,c =7,+,c =9}

=8 (we select A other that 1)+8((we select A other than 3)+8(...5)+8(...7)+8(...9)

=40

2.

(choose A)(choose B)(C=1) = (8)(7) (A and B not equal to 1 and not same) = 56

(choose A)(choose B)(C=3) = (8)(7) (A and B not equal to 3 and not same) = 56

(choose A)(choose B)(C=5) = (8)(7) (A and B not equal to 5 and not same) = 56

(choose A)(choose B)(C=7) = (8)(7) (A and B not equal to 7 and not same) = 56

(choose A)(choose B)(C=9) = (8)(7) (A and B not equal to 9 and not same) = 56

so total number of possible ways = 40 +56(5)= 40 + 280 =320

A B C

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