Solution : [i] When repetition of digits is allowed:
No. of ways of choosing firsy digits = 5
No. of ways of choosing second digit = 5
No. of ways of choosing third digit = 5
Therefore, total possible numbers `= 5 xx 5 xx 5 = 125`
[ii] When repetition of digits is not allowed:
No. of ways of choosing first digit = 5
No. of ways of choosing second digit = 4
No. of ways of
choosing thrid digit = 3
Total possible numbers `= 5 xx 4 xx 3 = 60`.
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Solution
Given 3 digit numbers that can be formed using the digits from 1 to
9.
Required number of 3-digit numbers= arranging
3 digits with the total number of 9 digits.
=
9P3=[9×8×7]=504.
Hence, the required number of numbers
=504.
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How many possible 3 digit numbers can be made using the digits 604?
There are 4 possible numbers if the digits are not repeated; 18 if they are. Those are 3-digit numbers, assuming that zero would not be a leading digit. If zero is allowed for a leading digit, then you can have 6 for the non repeated, and 27 if repetition.
Thea E. how many three digit numbers can be made with the digits 1,2,3,4,5,6 and 7 if a] repetitions are allowed b] no digits is to be repeated in a number? More
1 Expert Answer
Hi Thea
With 7 numbers, we can create three digit numbers like this.
a] With repetitions would suggest with replacement.
We'd have 7 options for the first digit, 7 options for the 2nd digit and 7 choices for the 3rd digit
73 = 343 combinations
b] Without repeated numbers, would suggest without replacement
We'd have 7 options for the first digit, 6 options for the 2nd digit and 5 choices for the 3rd digit
7•6•5 = 210 combinations
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