Question

A code consists of four characters:

Ø The first character must be a letter of the English alphabet

Ø The other three characters must be a digit

Find the number of ways in each of the following:

a)  Codes

b) Codes beginning with a vowel letter

c)  Digits cannot be repeated

Answer 1

a) 26 variants to choose letter, 10 variants to choose one digit. Means

$26*10*10*10=26000$ variants of code(if lower case and uppercase is different 52000 variants)

b) 6 variants to choose vowel letter (if y is vowel), 10 variants to choose one digit. Means

$6*10*10*10=6000$ variants of code(if lower case and uppercase is different 12000 variants)

c) 26 variants to choose letter, 10 variants to choose one digit, 9 variants to choose another digit and 8 to choose one another. Means

$26*10*9*8=18720$ variants of code(if lower case and uppercase is different 37440 variants)