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

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

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