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  • The number of 5-digit integers formed by the digits 0,3,4,5,6,8 in the interval [3502, 5472] isOption: 1 4855<div c

The number of 5-digit integers formed by the digits 0,3,4,5,6,8 in the interval [3502, 5472] is

Option: 1

4855


Option: 2

3955


Option: 3

5455

 


Option: 4

6595


Answers (1)

best_answer

Given that,

The number of 5-digit integers formed by the digits 0,3,4,5,6,8 in the interval [3502, 5472].

Let us consider the 1st digit as A, the 2nd digit as B, the 3rd digit as C, the 4th digit as D, and the 5th digit as E.

Position A has the digits 3, 4, and 5.

If the digits 0, 6, and 8 are put in position A then it will not be in the range [3502, 5472].

So, position A can be filled with 3, 4, and 5 in ^{3}C_{1}=3^{3}C_{1}=3 ways.

Position B can be filled with any one of the digits 0, 3, 4, 5, 6, and 8 in ^{6}C_{1}=6 ways.

Position C can be filled with any one of the digits 0, 3, 4, 5, 6, and 8 in ^{6}C_{1}=6 ways

Position D can be filled with any one of the digits 0, 3, 4, 5, 6, and 8 in ^{6}C_{1}=6 ways.

Position E can be filled with any one of the digits 0, 3, 4, 5, 6, and 8 in ^{6}C_{1}=6 ways.

Thus, the number of ways of the number starting with 3, 4, and 5 is given by,

3\times 6\times 6\times 6\times 6=3888

Now, we have to find the number which starts with 3 and 5 but doesn’t fall in the range [3502, 5472].

The possible way of starting the number with 300 is 6.

Placing 0 in the last place in 3502 will be less than the range.

So, the possible way is 1.

Considering the number 5472, here the 2nd place is filled with 5 or 6 will go beyond the range. In the 3rd place, any of the 6 digits can be placed.

So, the possible way is 2\times 5\times 6\times =60.

The total number which starts with 3 and 5 but doesn’t fall in the range is,

6+1+60=67

Therefore, the total number falls in the range is 3888+67 = 3955.

 

Posted by

rishi.raj

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