A new quarterback has to pick two number that will go on his football shirt. How many pair of number can be make from the digits 3,5,7,and 9? What are all the possible choice?Explain how you arrived at your answer.
4 choices for the first digit, leaving 3 choices for the 2nd digit.
What is 4 x 3 ?
You might try listing all the possible cases, there are only 12 of them
there are 4 choices for each digit. So there are 4*4 = 16 pairs possible.
Now, if there are no repeats, then there are 4 choices for the 1st, but only 3 for the second, making 4*3 = 12 possible numbers.
Go with Steve's solution, since there was no mention of "no repeats allowed."
I sort of imagined the numerals 3, 5, 7, and 9 lying there to be sewn on the jersey.
To find the number of pairs that can be made from the digits 3, 5, 7, and 9, we will use the concept of combinations.
First, let's list the digits: 3, 5, 7, and 9.
To create pairs, we choose two digits from this set. We can solve this by calculating the number of combinations of 4 digits taken 2 at a time.
The formula for combinations is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of options and r is the number of items chosen.
Using the formula, we can calculate the number of combinations of 4 digits taken 2 at a time:
C(4, 2) = 4! / (2!(4-2)!),
= 4! / (2!2!),
= (4*3*2*1) / [(2*1)(2*1)],
= 24 / 4,
= 6.
So, there are 6 different pairs that can be made from the digits 3, 5, 7, and 9.
Now, let's determine all the possible choices:
The possible pairs are:
- (3, 5)
- (3, 7)
- (3, 9)
- (5, 7)
- (5, 9)
- (7, 9)
These are all the valid pairs that can be made using the digits 3, 5, 7, and 9.