Four digit numbers with all digits distinct are formed using the digits 1,2,3,4,5,6,7 in all possible ways. If p is the total number of numbers thus formed and q is the number of numbers greater than 3400 among them, then p: q=

Step-by-step solution

p= Total four digit number's formed using 1,2,3,4 , 5,6,7= ^7 C₄ 4!= 7!4! 3!4! =840 For number greater than 3400 , Numbers starting with 3,4 are = ^5 C₂ 2!=20 Now, first digit can be 4,5,6,7= ^4 C₁ ^6 C₃ 3!=480 Numbers starting with 3 and second digit 5, 6, 7 are = ^3 C₁ ^5 C₂ 2!= 3! 5! 3!2! =60 q= Total numbers greater than 3400=20+480+60=560 Now, p: q=840: 560=3: 2 .