Respuesta :
We want to make a banner with a string of n-inch-long letters. The letters we want to use come in the following widths:
Step-by-step procedure:
Given the folowing letters with the following widths.
1 inch = f,i,t = 3 letters
2 inch = a,c,d,e,g,n,o,p,s,u = 10 letters
Since the minimum width is 1 inch, we cannot make any string with widh zero inches.
For 1 inch :
We have 3 letters of one inch. We can use them one at a time . So the answer is 3 ways
For 2 inch :
We can either use one letter of two inches, or two letters with one inch : we get , 10 + 3^2 ways. because repitition is allowed. So we have 19 ways.
For 3 inch :
So we will use one letter of 2 inches and one of 1 inch, or three letters of 1 inch. Order also matters so we can use permutations (not combinations).
_{1}^{10}\textrm{P}._{1}^{3}\textrm{P}.2 + 3^3
87
For 4 inch :
We can take either 2 letters from two inches, 1 from 2 inch and 2 from 1 inch or 4 from one inch, we get :
10^2 + 10(3^2).3 + 3^4
451
The second term is multiplied by three because I can put the 2 inch letter in three positions (1st, 2nd, 3rd..)
To learn more about string of letters, visit: https://brainly.com/question/28165987
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