If the number of 7 digit numbers whose sum of the digits is equal to 10 and which is formed by using the digits 1 , 2 and 3 only is K , then the value of K + 46 100 is

Step-by-step solution

In a 7 digits number formed by using 1 , 2 and 3 suppose that 1 appears x times, 2 appears y times and 3 appears z times. Then x + 2 y + 3 z = 10 and x + y + z = 7 ⇒ y + 2 z = 3 ⇒ y = 1 , z = 1 or y = 3 , z = 0 ⇒ x = 5 , y = 1 , z = 1 or x = 4 , y = 3 , z = 0 Therefore, the total number is 7 ! 5 ! + 7 ! 4 ! 3 ! = 42 + 35 = 77 ⇒ k = 77 ⇒ k + 46 100 = 77 + 46 100 = 1.23