How many numbers higher than a million can be formed with the digits 0,4,4,5,5,5,3?
Answers
Answer:
270
Step-by-step explanation:
1 million = 1000000
number greater than 1000000
1st Digit can be any of the digit from 3 , 4 , 5
Hence 3 Ways
Case 1 : First Digit 3
Remaining 6 Digits = 6!/2!3! (as 4 repeated thrice & 5 repeated thrice)
= 60
Case 2 : First Digit 4
Remaining 6 Digits = 6!/3! (as 5 repeated thrice)
= 120
Case 3 : First Digit 5
Remaining 6 Digits = 6!/2!2! (as 4 & 5 repeated twice)
= 90
Total Possible numbers = 60 + 120 + 90 = 270
Answer:
360
Step-by-step explanation:
How many numbers higher than a million can be formed with digits 0,4,4,5,5,5,3?
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360
Let’s start with all the permutations of these 7 items. Normally that would be 7! (7 factorial, i.e., 7*6*5*4*3*2). But, in this case, we must eliminate the possibility of a leading zero since all such arrangements would NOT be “higher than a million.” So, we need to altar the number of possibilities for the first slot; this would give us 6*6*5*4*3*2 (which is 6*6!).
But this would include many duplicate arrangements since there are two 4s and three 5’s. The effect of this duplication is to increase beyond the number of acceptable arrangements by this factor: (2!*3!), which is just (2*3!). So we need to divide by that factor to get a true result. So, with all this taken into account, here is our final calculation:
(6*6!) / (2*3!) = 360