A licence plate starts with 3 letters. If possible letters are M, N, P, Q, R, S, T. How many different permutation of these letters can be made if no letter used more than once.
7P3, right?
oh ok, thanks
To find the number of different permutations of these letters, we have to multiply the number of choices for each position.
Since there are 3 positions and each position can be filled with 7 possible letters (M, N, P, Q, R, S, T) without repetition, the number of different permutations can be calculated as follows:
Number of choices for the first position = 7
Number of choices for the second position = 6
Number of choices for the third position = 5
Therefore, the total number of different permutations is:
7 * 6 * 5 = 210
So, there are 210 different permutations of these letters that can be made if no letter is used more than once.
To find the number of different permutations of these letters, you can use the concept of permutation formula.
Since there are 3 positions for the letters on the license plate, you need to calculate the number of permutations of 3 letters chosen from 7 options.
The formula for permutations is given by:
nPb = n! / (n - b)!
Where n represents the total number of options and b represents the number of positions.
In this case, n = 7 (since there are 7 possible letters) and b = 3 (since there are 3 positions).
Let's calculate the number of permutations:
7P3 = 7! / (7 - 3)!
= 7! / 4!
= (7 * 6 * 5 * 4!) / 4!
= (7 * 6 * 5)
= 210
Therefore, there are 210 different permutations of the given letters that can be made for the license plate.