Question

How many permutations can be made from the letters m, n, o, p, and q taken 3 at a time?

6
30
60

Answer 1

60 permutations

Explanation:

Number of permutation from letters m, n, o, p, and q taken 3 at a time

Having number of letters to be (m,n,o,p,q) = 5

And 3 of them can be taken as a time.

These implies that 3letter can be taken at once irrespective of their arrangement which will serve as the first picking, the 4th letter will be the second picking and the 5th letter will be the third picking

To get the number of permutation (arrangement) for this.

Formular = nPr = n! / (n-r)!

Where in this case n = 5, r = 3

Therefore

5P3 = 5! /(5 - 3)!

= 5! / 2!

= 5*4*3*2*1/2*1

= 60 permutations

Answer 2

There are 5 letters m, n, o, p and q.
These letters can be arranged 5! ways.
5!=5×4×3×2×1=120
Now you are taking 3 at a time.
So, 5!/3!=120/6
Now multiply this by 3.
20×3=60.