How many 5 digit numbers are there such that the number are in strictly decreasing order?
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If m denotes the number of 5 digit numbers 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 value.A. ${}^{24}{C_4}$B. ${}^9{C_5}$C. ${}^{10}{C_5}$D. ${}^9{C_3}$Answer 
Hint- In order to solve this first separately use the concept of permutation and combination to find the figure for descending order of the numbers and ascending order of numbers. Finally subtract the results and use the formula for the subtraction of combination of terms to get the correct answer amongst the given options.Complete answer: Note- In order to solve these types of problems, first of all remember all the formulas of combination. Also remember the properties of combinations. The next step is to read the statement carefully and write the conditions given in the questions and solve accordingly. You must have a good command on algebra to and algebraic identities.
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How many five digit decreasing numbers are there?= 7*8*8*8*8 = 28,672 Answer.
How many 5 digit number divisible by 5 can be formed from the digits?Thus, the total number of five digit numbers divisible by 5 is 120+96=216.
How many 5 digit numbers with distinct digits are there such that in each number the digits are in descending order from left to right?And, for the descending order, you can have 0 in the number, and it would be placed at the end, thus not affecting the no. of digits in the number. So, there are 10 digits to choose from, and hence there can be 10C5=252 5-digit no. s with their digits in a descending order.
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