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If 'm' denotes th e no of 5-digit nos, if each successive digits are in their descending order of magnitude and 'n' is the corresponding figure, when the digits are in their ascending order of magnitude then (m-n) has the value.....?

If 'm' denotes th e no of 5-digit nos, if each successive digits are in their descending  order of magnitude and 'n' is the corresponding figure, when the digits are in their ascending order of magnitude then (m-n) has the value.....? 

Grade:12

1 Answers

Askiitians Expert Bharath-IITD
23 Points
11 years ago

Finding out the number of 5 digit numbers having digits in descending order:-

1)digits staring with 9--the next 4 digits can accommodate digits from 0 to 8 only.these can be selected in 9C4 ways and arranged in descending order and there is only one way of arranging the selected 4 numbers in descending order.

Eg:one of the sets formed is (8,0,3,5)

its descending order is 8530.the number is 98530.i.e.,only one way.

so number of 5 digit numbers formed are 9C4.

2)digits starting with 8--next 4 digits can have numbers from 0 to 7 only.these can be selected in 8C4 ways.

similarly digits starting with 7,6,5,4 gives 7C4+6C4+5C4+4C4.

m=9C4+8C4+7C4+6C4+5C4+4C4

 

Finding out number of 5 digit numbers having digits in ascending order:-

These cant start with 0

1)so,numbers starting with 1--next 4 digits can have digits from 2 to 9 only.so can be selected in 8c4 ways.

2)numbers starting with 2--7C4.

Similarly we can find numbers with 3,4,5

n=8C4+7C4+6C4+5C4+4C4

m-n=9c4=126 

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