A 7-digit number is formed using the digits from 1 to 9 (without repetition) such that its digits are in strictly increasing order from left to right. If the middle digit (the 4th digit from the left) is exactly 5 , then the total number of such 7-digit numbers that can be formed is :

Step-by-step solution

Let the 7-digit number be d₁ d₂ d₃ d₄ d₅ d₆ d₇ . Given that the digits are in strictly increasing order, d₁ We are given that the middle digit d₄ = 5 . The three digits before 5 ( d₁, d₂, d₃ ) must be chosen from the digits strictly less than 5 , which are 1, 2, 3, 4 . The number of ways to select these 3 digits is ⁴C₃ = 4 . The three digits after 5 ( d₅, d₆, d₇ ) must be chosen from the digits strictly greater than 5 , which are 6, 7, 8, 9 . The number of ways to select these 3 digits is ⁴C₃ = 4 . Once the digits