Question

How many combinations exist for the letters m, n, o, p, and q taken 3 at a time?

1) 60
2) 10
3) 20

Answer 1

The number of combinations for the letters m, n, o, p, and q taken 3 at a time is 10, as calculated using the combinations formula nCr = n! / (r! * (n-r)!).

Step-by-step explanation:

The question is asking about the number of combinations of the letters m, n, o, p, and q taken 3 at a time. In the world of combinatorics, a branch of mathematics, the formula for finding the number of combinations (without repetition) is given by:

nCr = n! / (r! * (n-r)!)

where n is the total number of items, r is the number of items being chosen, and the exclamation point (!) denotes a factorial.

Applying this to our case:

n = 5 (the letters m, n, o, p, and q)
r = 3 (the number of letters to choose at a time)

Therefore:

5C3 = 5! / (3! * (5-3)!)
5C3 = (5*4*3*2*1) / ((3*2*1) * (2*1))
5C3 = (5*4) / 2
5C3 = 10

So, there are 10 combinations possible.