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The number lock of a suitcase has 4 whee...

The number lock of a suitcase has 4 wheels, each labelled with ten digits from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the sequence to open the suit case?

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There are 10 digits viz, .0,1,2, ldots ldots ldots .9. Thousand.s place number can be selected in 10 ways. 100 .s place number can selected in 9 ways. 10.s place number can be selected in 8 ways and l.s place can be filled in by 7 ways. Therefore, the total number of ways to open the lock .=10 xx 9 xx 8 xx 7. So probability of a person getting the sequence to open the suitcase .=1/10 xx 9 xx 8 xx 7=1/5040.
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Consider the number 2751. The sum of its digital is 2+7+5+1=15 . Adding the digits of 15 we get 1+5=6 . This number 6 is called the 'digital root' of the number 2751. That is, to find the digital root of a number, find the sum of its digits (Don't forget to find the sum of the digits again, if the first sum has more than one digit) Let us see one more example. The sum of the digits of the numbe 679412 is 6+7+9+4+1+2=29 . Sum of digits of 29=2+9=11 . Sum of digits of 11=1+1=2 . Therefore the digital root of 679412 is 2 . Digital roots have an interesting property. To see this, consider the product 43times27=1161 . The digital roots of the numbers 43 and 27 are 4+3=7 and 2+7=9 . Product of the digital roots= 7times9=63 . Digital root of 63=6+3=9 . The Digital root of 1161 is also 9(1+1+6+1=9) that is the digital root of 1161 =The digital root of 63 , where 63 is the product of the digital roots of 43 and 27. This property is true for all other natural numbers. If the digital root of a is 5 and the digital root of b is 2. Then what is the digital root of ab ?

Consider the number 2751. The sum of its digital is 2+7+5+1=15 . Adding the digits of 15 we get 1+5=6 . This number 6 is called the 'digital root' of the number 2751. That is, to find the digital root of a number, find the sum of its digits (Don't forget to find the sum of the digits again, if the first sum has more than one digit) Let us see one more example. The sum of the digits of the numbe 679412 is 6+7+9+4+1+2=29 . Sum of digits of 29=2+9=11 . Sum of digits of 11=1+1=2 . Therefore the digital root of 679412 is 2 . Digital roots have an interesting property. To see this, consider the product 43times27=1161 . The digital roots of the numbers 43 and 27 are 4+3=7 and 2+7=9 . Product of the digital roots= 7times9=63 . Digital root of 63=6+3=9 . The Digital root of 1161 is also 9(1+1+6+1=9) that is the digital root of 1161=The digital root of 63 , where 63 is the product of the digital roots of 43 and 27. This property is true for all other natural numbers. What is the digital root of 345?

Consider the number 2751. The sum of its digital is 2+7+5+1=15 . Adding the digits of 15 we get 1+5=6 . This number 6 is called the 'digital root' of the number 2751. That is, to find the digital root of a number, find the sum of its digits (Don't forget to find the sum of the digits again, if the first sum has more than one digit) Let us see one more example. The sum of the digits of the numbe 679412 is 6+7+9+4+1+2=29 . Sum of digits of 29=2+9=11 . Sum of digits of 11=1+1=2 . Therefore the digital root of 679412 is 2 . Digital roots have an interesting property. To see this, consider the product 43times27=1161 . The digital roots of the numbers 43 and 27 are 4+3=7 and 2+7=9 . Product of the digital roots= 7times9=63 . Digital root of 63=6+3=9 . The Digital root of 1161 is also 9(1+1+6+1=9) that is the digital root of 1161=The digital root of 63 , where 63 is the product of the digital roots of 43 and 27. This property is true for all other natural numbers. What is the digital root of 927?

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