consider the set of S of strings of seven letters from the a

consider the set of S of strings of seven letters from the alphabet. That is, each position is occupied by one of the 26 lowercase letters. Each letter may appear more than once in S. This set, and the subsets listed below, can be counted using trees. You may give your answer as a product, to indicate how you found the formula.

(A) . What is the size of S?

(B). In how many members of S is no letters x,y, and z excluded?

(C). in how many members of S is a no letter repeated?

(D). In how many members of S does the letter z occur three times?

(E). In how many members of S do the third and fifth letter agree?

Solution

a)

size of S-------> 7 letters from thealphabet

b)

we have 26 letters and we need to choose 7 BUT THE LEETER CAN APPEAR MORE THAN ONCE

but there is an excluded 3 letters so we are going to choose 7 letters from 26-3 = 23

the formula for combination with repeat is n+r-1 C r

23+3 -1 C 3 = 2300

c)

a letter no repeated so this is

26 C 3 = 2600

d and e)

for this lterals

I can gladly help you but you should post it in a new question