Question

How many 2-letter combinations can be created from the distinct letters in the word “mathematician”? Assume that the order of the letters does not matter.

Answer 1

Answer:

The total number of 2-letter combinations can be created from the distinct letters in the word mathematician=28.

Step-by-step explanation:

We are given that a word "mathematician".

We have to find the number of  2-letter combinations can be created from the distinct letters in the given word.

We have total letters in the word mathematician =13

Total number of distinct letter in the word mathematician =m,a,t,h,e,i,c,n=8

We have find the total number of combination of 2 letters out of 8 distinct letter by using combination formula

Combination formula:

$\binom{n}{r}=\frac{n!}{r!(n-r)!}$

We have n=8 and r=2

Therefore , total number of combination from 2 -letters out of 8 letters=$\binom{8}{2}=\frac{8!}{2!(8-2)!}$

The total number of combinations from 2-letters out of 8 distinct letters =$\frac{8\times7\times6!}{2!\times6!}=\frac{8\times7}{2\times1}$

The total number of combinations from 2 -letters out of 8 distinct letters=$=4\times7=28$.

Hence, the number of 2-letters combinations  can be created from distinct letters in the word mathematician =28.

Answer 2

Hello!

this problem comes with a slightly complex math equation that I had to ask my math teacher about, so I hope it helps.

The expression n! means "the product of the integers from 1 to n"
this can be said for any variable

say n is the total and r is the 2-letter combo

C(n,r)=13!/(2!(13−2)!)

If you use this equation, you will get a final answer of: 78

I hope this helps, and have a nice day.