If all possible numbers are formed by using the digits 1 ,   2 ,   3 ,   5 ,   7 without repetition and they are arranged in descending order, then the rank of the number 327 is

Step-by-step solution

Given numbers are 1 ,   2 ,   3 ,   5 ,   7 . And also they are arranged in descending order. i.e., the numbers with four and five digits are included. The number of five-digit number = 5 ! The number of four digits number = p 4 5 = 5 ! ( 5 - 4 ) ! = 120 1 = 120 The number of 3 digits starting with 7 = i.e., 4 digits have to be fit in 2 place in p 2 4 ways, p 2 4 = 4 ! ( 4 - 2 ) ! = 4 × 3 = 12 The number of 3 digits numbers starting with 5 = p 2 4 = 4 ! ( 4 - 2 ) ! = 4 × 3 = 12 The num