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

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.

Answer 2

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

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}=(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}=(8!)/(2!(8-2)!)`

The total number of combinations from 2-letters out of 8 distinct letters =
`(8*7*6!)/(2!*6!)=(8*7)/(2*1)`

The total number of combinations from 2 -letters out of 8 distinct letters=
`=4*7=28`.

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