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)
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 1st 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 1st digit and repetition is allowed
"=5\\times 7\\times 7\\times 7\\times 7=12005" ways
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