1) Suppose that a company will select 3 people from a collection of 15 applicants to serve as a regional manager, a branch manager, and an assistant to the branch manager. In how many ways can the selection be made? Explain how you got your answer.
15 15Pz= = 15 - 14 - 13 = 2,730
2) How many distinguishable permutations can be made of the letters in the word POSSIBILITIES? Explain how you got your answer.
In the word POSSIBILITIES there are only two repetitive letters S and I, containing 3 S's and 4 13! I's. The equation will look something like: which is calculated to be 43,243,200. 4!3!
3) There are two display cases, one with 18 flowers and one with 15 flowers. How many ways can you choose 3 flowers from the first case and 2 from the second case?
n! n! I use the equations C - r! = ,P, = and C = (n-r)! r!(n-r)!
Task 1 is to choose 3 flowers from the case with 18 flowers in it & Task 2 is to choose 2 flowers from the case with 15 flowers in it
18! In the first task the equation will look something like this: 1:C which equals . After 3!15! calculating, this turns out to be 816 ways to choose 3 flowers from a case with 18 flowers in it.
15! In the second task the equation will look something like this: 15C, which equals 2!13! After calculating, this turns out to be 105 different ways to choose 3 flowers from a case with 18 flowers in it.
In order to find the number of ways there are to choose 3 flowers from the first case and 2 from the second, you would multiply the number of ways there are from each task, which would be 816 : 105 which equals 85,680.
4) A fair 6fisided die is rolled 5 times and the result is recorded for each roll. a) How many different sequences of results are possible? Explain how you got your answer.
Since the dice has 6 sides and is being rolled 5 times, the number of different sequences that are possible are 6' or 7776 possible different sequences.
b) Of the possible sequences of results, how many of them contain exactly 3 rolls of a 4? Explain how you got your answer. Since we are looking for how many possible sequences contain exactly 3 rolls of a 4, 5 the first thing I would do to my equation is: , which equals 10.
I would then take the first part of the equation and multiply it by 52, because after the 3 rolls that will contain a 4, there are still 2 rolls left in the sequence.
5!52 The equation would look like: 3!2! which would contain 3 rolls of a 4.
which can be calculated out to be 250 rolls
5) Show that if 17 integers from 1 to 32 are chosen, then there will be 2