Answer: The required number of combinations is 10.
Step-by-step explanation: We are given to find the number of combinations that exists for the letters m, n, o, p, and q taken 3 at a time.
We know that
the formula for the combination of s objects taken r at a time is given by
[tex]^sC_r=\dfrac{s!}{r!(s-r)!}.[/tex]
For the given combination, we have 5 letters and we are to take 3 at a time.
So, s = 5 and r = 3.
Therefore, the required number of combinations is
[tex]^5C_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!2!}=\dfrac{5\times4\times3!}{3!\times2\times1}=10.[/tex]
Thus, the required number of combinations is 10.
