Five digit numbers are formed from digits 4, 5, 6, 7 and 8. (a)How many such numbers can be formed if repitition of digits is (i) allowed (ii) not allowed? ...
Question 1 Report
Five digit numbers are formed from digits 4, 5, 6, 7 and 8.
(a)How many such numbers can be formed if repitition of digits is (i) allowed (ii) not allowed?
(b) How many of the numbers are odd, if repetition of digits is not allowed?
Answer Details
Five different digits are available: \(4, 5, 6, 7, 8\).
(a)(i) Repetition allowed: each of the 5 positions can be any of the 5 digits:
\[5^5 = 3125\](ii) Repetition not allowed: arrange all 5 distinct digits:
\[5! = 120\](b) A number is odd if its last digit is odd. Among the digits, the odd ones are \(5\) and \(7\), giving 2 choices for the units position. With no repetition, the remaining 4 positions are filled by the remaining 4 digits in \(4!\) ways:
\[2 \times 4! = 2 \times 24 = 48\]So 48 of the numbers are odd.
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