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.

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 Link

lublana lublana · Answer 2 · 2019-07-18T11:09:20+02:00

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:

[tex]\binom{n}{r}=\frac{n!}{r!(n-r)!}[/tex]

We have n=8 and r=2

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

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

The total number of combinations from 2 -letters out of 8 distinct letters=[tex]=4\times7=28[/tex].

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