Question #194157

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 1st digit and repetition is not allowed?

(3 pts)

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

 


1
Expert's answer
2021-05-19T17:31:43-0400

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


(a) Repetition is allowed-

=6×7×7×7×7=14406= 6\times 7\times 7\times 7\times 7=14406 ways


(b) Repetition is not allowed

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


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


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


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


=5×7×7×7×7=12005=5\times 7\times 7\times 7\times 7=12005 ways


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