Question

let A be the set of 4 digit number a1a2a3a4 where a1>a2>a3>a4 then how many values of A are possible?

Answer 1

START with 3 = 3_ _ _. You can fill in with digits 0,1,2. Hence 3C3 = 1 
START with 4 = 4_ _ _. (0,1,2,3). hence 4C3= 4 
START with 5, you have (0,1,2,3,4) to fill in the blanks behind 5, hence 5C3 = 10 
START with 6, 6C3=20 
7... = 7C3 = 35 
8...=8C3 = 56 
9...= 9C3 = 84 

Now you add up all the possible numbers, 1+4+10+20+35+56+84 =210.Therefore the number of 4 digit nos that can be formed is 210. The thing is u set the first digit as 3,4,5, and so on up till 9. then u permutate the second third and fourth digits. But in order to have decreasing order, there is only one way to permutate whatever combinations of digits that is possible after the first digit. hence u use combinations instead of permutations.Loh · 4 years ago