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How many 10-digit positive integers with distinct digits are multiples of 11111?
Wiki User
∙ 14y ago
-11101
Lorine Batz
Wiki User
∙ 14y agoSince digits of 10digits number n sum to 45 , n should be divisible by 9
n should be divisible by 99999
10 digits number will be of type n = 100000*x + y where x is 5digit number and y is 4 or 5 digit number
n = 99999*x + (x+y)
means x+y should be divisible by 99999
and because neither x > 99999 nor y>99999
x+y = 99999
x=abcde
y=pqrst
----------------------
x+y=99999
also since max numbers is 9 and 8 we cannot carry to next digit (19)
so it has to be all 9s without carry
groups
0 9
1 8
2 7
3 6
4 5
means combination is for x only. y is related
digit 1 : {1-9} 9ways
digit 2 : {digit1,0} - {digit1,9-digit1} 8 ways
digit 3 : {digit2} - {digit2.9-digit2} 6 ways
digit 4 : {digit3} - {digit3.9-digit3} 4 ways
digit 5 : {digit4} - {digit4.9-digit4} 2 ways
total ways : 9*8*6*4*2=3456
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