Question

How many strings of nine uppercase English letters are there

a. if letters can be repeated?   

b. if no letter can be repeated?

c. that start with the letters MN (in that order), if letters can be repeated?

d. that start and end with the letters MN (in that order), if letters can be repeated?

e. that start or end with the letters MN (in that order), if letters can be repeated?

Answer 1

a) number of ways =N(26 choices for each letter) =26⁹ =5429503678976

b) number of ways =26*25*24*23*22*21*20*19*18 =1133836704000

c) number of ways =N(choose rest of 7 letters) =8031810176

d) . that start and end with the letters MN =26⁵ =11881376

e) N( that start or end with the letters MN ) =N(start with)+N(end with)-N(start and end)=26⁷+26⁷-26⁵ =16051738976