Question 217297: kindly answer this question please!!! Thanks!!! Four numbers are to be formed from the digits 1,2,3,4,5,6,7 with no repetition allowed A.How many are less than 5000? B.How many are greater than 6000?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 4 number from the digits 1,2,3,4,5,6,7
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Number shown is less than 5000:
5,6,7 in the first position are not allowed.
That leaves 1,2,3,4 that can be in the first position.
All other positions can be filled with the remaining digits.
The number of possible ways this can happen is:
4*6*5*4 = 480 ways.
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Number shown is greater than 6000:
1,2,3,4,5 in the first position are not allowed:
That leaves 5,6,7 that can be in the first position.
All other positions can be filled with the remaining digits.
The number of possible ways this can happen is:
3*6*5*4 = 360 ways.
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to make this easier to show, assume the number of digits is 3 that can be picked from the numbers 1,2,3,4
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Number of ways the numbers can be less than 300 would be 2*3*2 = 12
Those possible ways would be:
123
124
132
134
142
143
213
214
231
234
241
243
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Number of ways the numbers can be greater than 400 would be 1*3*2 = 6
Those possible ways would be:
412
413
421
423
431
432
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Same concept applies to larger numbers.
It's the number of possible ways for the first digit times the number of possible ways for the second digit times the number of possible ways for the third digit times the number of possible ways for the fourth digit.
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The number of possible ways for the first digit was determined by the range of values allowed.
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If the first number was less than 5000, then the only digits allowed were 1,2,3,4 which made the total possible of ways for the first digit = 4.
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If the first number was greater than 6000, then the only digits allowed were 6,7,8 which made the total possible of ways for the first digit = 3.
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the number of possible ways for each succeeding position was the number of remaining digits left. That was 6 for the second position, 5 for the third position, 4 for the fourth position.
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This assumed no digits could be reused. Once pulled from the pot, they were not returned.
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