Answer:
1-D)40
2-D
3-B)
4 There are 120 permutations.
5 There are 165 combinations.
6 Sample space is {HH,HT,TH,TT}
Step-by-step explanation:
Number 1
Step 1
The fundamental counting theorem states that for process that can be carried out in k steps where the fist step can be done in ways, step 2 can be done in
number of ways and the
can be done in
number of ways, the number of ways to complete this task is
ways.
Step 2
We now realize that this process can be carried out in 2 steps , there are 8 ways to complete the first step and 5 ways to complete the second step. The number of ways to carry out this calculation is shown below,
The correct answer is D.
Number 2
Step 1
in this step we calculate the number total number of cans in the ice chest. Since there are 30 red cans and 20 green cans, there is a total of 50 cans.
Step 2
In this step we find the probability of grabbing a green can by dividing the total number of green cans by the total number of cans. The calculation for the probability is shown below,
The correct answer is D.
Number 3
Step 1
The first step is to realize that there is a chance of getting a head when flipping a coin. When a die is rolled the sample space is {1,2,3,4,5,6}. From this we can tell that there are 3 out of 6 ways to get an even number from this sample space. The probability for an even number is
Step 2
The second step in this process is to realize that these two events are independent hence we multiply the individual probabilities of the different outcomes to get the odds of a head and an even number. This calculation is shown below,
The correct answer is D
Number 4
Step 1
The first step is to realize that the only unique letters in INNOVATIVE are {I,N,O,V,A,T,E}, i.e there are only seven unique permutations of these letters.
Step 2
The second step is to calculate the number of 4 permutations of 7 objects.
This is calculated as shown below,
There are 210 unique permutations of these letters.
Number 5
Step 1
Realize that the number of r combinations of n objects is ,
Step 2
We realize that in this problem we have to make 3 combinations of 11 objects. The calculation to determine the number of combination sis shown below,
Number 6
Step 1
We list the outcomes where we first get a head. These outcomes are {HH,HT}. Next we list the outcomes in which we get a tail first. These outcomes are {TH,TT }
Step 2
In this step we combine all the outcomes step 1. The combined list of outcomes is {HH,HT, TH, TT}