Question

COUNTING METHODS (15 pts)

1. How many 5-digit number can be formed from digits 0 – 6 if:

a.   If repetition is allowed? (3 pts)

b.   If repetition is not allowed? (3 pts)

c.    If one (1) is not to be used as the 1^st digit and repetition is not allowed?

(3 pts)

d.   If one (1) is not to be used as the 1^st digit and repetition is allowed? (3 pts)

 

Answer 1

Number of ways in which 5 digit number can be formed from digit 0-6 if-

(a) Repetition is allowed-

$= 6\times 7\times 7\times 7\times 7=14406$ ways

(b) Repetition is not allowed

$=6\times 6\times 5\times 4\times 3=2160$ ways

(c) one (1) is not to be used as the 1^st digit and repetition is not allowed-

$=5\times 6\times 5\times 4\times 3=1800$ ways

(d) one (1) is not to be used as the 1^st digit and repetition is allowed

$=5\times 7\times 7\times 7\times 7=12005$ ways