Question

how many three digit numbers can you make with the digits 3,6,7,and 9,using each digit only once in any number

Answer 1

Answer:

There is 24 possible 3 digit numbers using 3, 6, 7, 9 with no repeated digits.

Step-by-step explanation:

We need to find the amount of permutations of size 3 that can be made from a set of size 4. We can write this as 4_P_3.

We can use this formula to find the amount of permutations:

n_P_k = $\frac{n!}{(n - k)!}$

We fill in our values:

4_P_3 = $\frac{4!}{(4 - 3)!}$

4_P_3 = $\frac{4 * 3 * 2 * 1}{1}$

4_P_3 = 24

There is 24 possible 3 digit numbers using 3, 6, 7, 9 with no repeated digits.

Answer 2

There are 24 possible 3-digit numbers using 3, 6, 7, and 9 with no repeated digits.

What is the combination?

The arrangement of the different things or numbers in a number of ways is called the combination.

We need to find the number of permutations of size 3 that can be made from a set of size 4. We can write this as $^4C_3$

We can use this formula to find the number of permutations:

$^nC_p$ = $\dfrac{n!}{(n-p)!}$

We fill in our values:

$^4C_3=\dfrac{4!}{(4-3)!}$

$^4C_3=\dfrac{4\times 3\times 2}{1}=24$

Therefore, there are 24 possible 3-digit numbers using 3, 6, 7, and 9 with no repeated digits.

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