Question 1020987: If no digit is repeated in any number, how many four-digit numbers can be formed out of the digits 1, 2, 3, 4, 5, 6, 7? How many of these numbers will exceed 4000?
Answer by mathmate(429)   (Show Source):
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Question:
If no digit is repeated in any number, how many four-digit numbers can be formed out of the digits 1, 2, 3, 4, 5, 6, 7? How many of these numbers will exceed 4000?
Solution:
with no repetition, there are 7 choices for the first digit, 6 for the second, 5 for the third and 4 for the fourth for a total of 7*6*5*4=840 numbers.
If the number must exceed 4000, then the first digit must be 4,5,6,or 7.
Following the same logic above, there are 4*6*5*4=480 distinct numbers. However, since 4000 does not exceed 4000, so it must be subtracted from the list leaving 480-1=479 numbers.
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