Question 952993: how many 5-digit numbers of 1,2,3,4,5,6 and 7 the number must contain a 6 and must not contain a 5?
how many 5-digit numbers of 1,2,3,4,5,6 and 7. The digit 3 must be in the second position and the 4 in the third position. the number must contain a 6 and not a 5. no digit can repeat
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! how many 5-digit numbers of 1,2,3,4,5,6 and 7 the number must contain a 6 and
must not contain a 5?
I am assuming that we cannot repeat a digit.
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First we'll find the number of 4 digit numbers that do not contain a
5 or a 6 and then
multiply by the number of ways we can insert a 6 in each, which is 5 ways:
For example in the 4 digit number 2371 can have a 6 inserted in 5 ways:
62371, 26371, 23671, 23761, 23716
The number pf 4-digit numbers we can make from {1,2,3,4,7} is
5 ways to choose the 1st digit.
4 ways to choose the 2nd digit.
3 ways to choose the 3rd digit.
2 ways to choose the 4th digit.
5P4 = 5*4*3*2 = 120 ways.
Then we can insert a 6 to make a 5-digit number 5 ways:
Answer 6*360 = 2160 ways.
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how many 5-digit numbers of 1,2,3,4,5,6 and 7. The digit 3 must be in the
second position and the 4 in the third position. the number must contain a 6
and not a 5. no digit can repeat:
-34--
We can choose the place to put the 6 in 3 ways.
That leaves 2 blanks to fill, a leftmost blank and a rightmost blank.
We can choose the digit to put in the leftmost remaining blank in 3
remaining ways: {1,2,7}
We can choose the digit to put in the rightmost remaining blank in 2
ways.
That's 3*3*2 = 18 ways.
Edwin
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