The license plates in Eulerville are made of seven distinct characters, six of which are letters from A to Z inclusive and one of which is a digit from 0 to 9 inclusive. How many different Eulerville license plates include
the word “MATH” with those four letters consecutive and in that order?
I just need to figure out how to get it, because my way didn't seem correct.
I did 26 choose 6, since there are letters and the numbers aren't necessary to be counted, and when I computed it, I got: 26x25x24x23x22x21 choose 6!, which came out as 6630624/720, simplifying to 9209.2. I dont believe my answer is correct, given that I had a decimal point in my answer. Could anyone try to help me understand how to solve this?
MATH can sit in 4 positions
then there are 3 positions left , one has to be a number 10 choices
the other two positions can be a letter 26 x 26
but the number can be in one of three positions x 3
4 x 10 x 26 x 26 x 3 = 81120 (?)
Ok, so I checked the answer and it was 55,440, although I still don't know how to get it.
Cphill answer below..... I neglected the 'distinct' portion of the question
so it should be :
MATH can sit in 4 positions
then there are 3 positions left , one has to be a number 10 choices
the other two positions can be a letter 22 x 21 (since M A T H are already used)
but the number can be in one of three positions x 3
4 x 10 x 22 x 21 x 3 = 55440
Guest 21 mins ago
+128475 Note....for any plate..... the word "MATH" can appear in any one of 4 positions
Since the characters are distinct, I'm assuming that no letter can be repeated
In the other 3 positions, we can choose any of 22 remaining letters * any of 21 remaining letters * 10 digits and these can be arranged in 3! = 6 ways
So.....in this scenario, we have
4 * 22 * 21 * 10 * 3 =
55440 possible plates
