Question 1173431: tudent was asked to form two-digit numbers using the following digits: 0,1,2,3,4,5,6,7,
and 8.
How many ways can Two-digit numbers be formed from the digits above?
Can you help me with this?.... thank you so much
Repeating of digits are not allowed
Found 2 solutions by ewatrrr, ikleyn:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
9 numbers: 0,1,2,3,4,5,6,7,8
How many ways can Two-digit numbers be formed:
1st digit 8 choices (not 0)
2nd digit 9 choices (all)
8x9 = 72 the ways can Two-digit numbers be formed from the digits above
Repeating of digits are not allowed (11,22,33,44,55,66,77,88)
72-8 = 64 the ways can Two-digit numbers be formed from the digits above,
Repeating of digits are not allowed
Note:
Permutation method would work if 0 was not included with the digits given
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
The solution by @ewatrrr is ABSOLUTELY WRONG.
For your safety, ignore it . . .
I came to bring you the correct solution.
First digit can be any of the 8 given digits from 1 to 8 inclusive.
(notice that 0 (zero) can not be the first digit of a two-digit number).
Second digit can be any of the 9 given digits from 0 to 8 inclusive.
It gives us 8*9 = 72 potential candidates for two digit numbers.
From this amount, we should exclude two-digit numbers with repeating digits.
They are 11, 22, 33, 44, 55, 66, 77, and 88 - in all, 8 numbers must be excluded from 72.
It gives the ANSWER 72 - 8 = 64.
ANSWER. There are 64 two-digit numbers satisfying to imposed conditions.
Solved.
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