# For a course a student has to choose one novel to study from a list of six, one poem from a list of 4, one short story from a list of seven. How many different choices does the student have?

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### 5 Answers

If a student has to choose one novel from a list of six, he has 6 choices for a novel.

If (s)he has to choose one poem from a list of 4, he has 4 choices for a poem.

Likewise, s(he) has 7 choices for a short story.

Choosing a novel, a poem, and a short story are independent events. This means that the choice of a novel does not affect at all the choice of either short story or a poem. In this case, for any choice of a novel, 4 different choices of a poem are possible, and for any given choice of a novel and a poem, 7 different choices of a short story are possible.

Therefore, to find the total number of choices, multiply the number of choices for a novel, a poem, and a short story:

6*4*7 = 24*7 = 168.

**The student has 168 different choices.**

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Is there a formula that I need to show?

If you want to apply a formula it can be n1 x n2 x n3 ...... ways.

In this case

n1=6

n2=4

n3=7

6*4*7=168

You can also apply the formula of combinations or permutations which will result in the same answer in this question:

Combinations (if order is not necessary then this is applied):

where,

n=total number 6,4,7

r=number of times 1,1,1

6C1 * 4C1 * 7C1

6*4*7= 168

Permutation (if order is necessary then this is applied):

6P1 * 4P1 * 7P1

6*4*7=168

Since the number of times is only one then these formulas will not be used, if number of times would have been more than one than one of these formulas would have been used.

If you want to apply a formula it can be n1 x n2 x n3 ...... ways.

In this case

n1=6

n2=4

n3=7

6*4*7=168

You can also apply the formula of combinations or permutations which will result in the same answer in this question:

Combinations (if order is not necessary then this is applied):

where,

n=total number 6,4,7

r=number of times 1,1,1

6C1 * 4C1 * 7C1

6*4*7= 168

Permutation (if order is necessary then this is applied):

6P1 * 4P1 * 7P1

6*4*7=168

Since the number of times is only one then these formulas will not be used, if number of times would have been more than one than one of these formulas would have been used.

For a course a student has to choose one novel to study from a list of six, one poem from a list of 4, one short story from a list of seven. How many different choices does the student have?

To figure out the choices, multiply by the possibilities:

6 x 4 x 7 = 168

If you're feeling adventurous, try working out all possible combinations using smaller numbers (say, 1, 2, 3) and then you'll realize why this works.

The "rule" used here can be formally called "The Multiplication Rule": *Suppose we can do job 1 in p ways, and for each of these ways, we can do job 2 in q ways. Then we can do both job 1 AND job 2 in p x q ways*"

So in this case, the first job is choosing a novel from the six. Then for** each** novel we choose, we have 4 ways of choosing a poem. For each poem, we have a choice of 7 short stories. Each of the things to study is a "job" and so the total number of choices is 6 x 4 x 7 = 168

For these problems all you have to do is multiply the numbers of each type you have together to get the total amount of choices. So since you have 6 choices for a novel, 4 choices for a poem, and 7 choices for a short story you would just multiply 6*4*7. This gives you 168 options. I don't think there is a specific formula for this you just show that you multiplied all the options together.