A five digit security code consists of five digits chosen fr

A five digit security code consists of five digits chosen from: 26 uppercase letters, 26 lowercase letters, and numbers {1,...,25}.

a) How many five digit codes are there?

b) How many six digit codes are there?

Solution

Total number of letters = 26+26+25=87

a) out of 87,we have to select 5 letters

number of ways = 87C₅

now these 5 letters will be arranged in 5! ways

total number of ways=87C₅ *5!=87P₅

b)

out of 87,we have to select 6 letters

number of ways = 87C6

now these 6 letters will be arranged in 6! ways

total number of ways=87C₅ *6!=87P₆

Note: here I considered that the repition of letter is not allowed