3 years ago
How many strings of six lowercase letters from the English alphabet contain 6(a) the letter a? 6(b) the letters a and b, where a is somewhere to the left of b in the string, with all the letters distinct
2 Answers
Best Answer
ashtonmullens Staff answered 3 years ago
ashtonmullens Staff answered 3 years ago
Step 1
c) 5, 12, 21, 32,...
first term
t_1=5=4(1)+1=4(1)+1^2
second term
t_2=12=4(2)+4=4(2)+2^2
third term
t_3=21=4(3)+9=4(3)+3^2
fourth term
t_4=32=4(4)+16=4(4)+4^2
n^th term t_n=4(n)+n^2
c) 3, 8, 17, 30,...
first term
t_1=3=3(1)+2(0)^2
second term
t_2=8=3(2)+2(1)^2
third term
t_3=17=3(3)+2(2)^2
fourth term
t_4=30=3(4)+2(3)^2
n^th term t_n=3(n)+2(n-1)^2
Best Answer
arsh1928 Staff answered 3 years ago
arsh1928 Staff answered 3 years ago
The reason is because 26^6 is the list of all strings of length five, and while there are six different ways to insert an "a" into each of those strings, some of those strings already have an "a" or more than one "a" in them. We don't want to use 25^5*6 either as this doesn't include strings that have more than one "a". The easiest way is to count all the strings of length six 26^6 and remove those that don't have an "a" in them 25^6