Question

The number of 4 digit even numbers whose sum of digits is 34

• A. 5
• B. 12
• C. 3
• D. 7

Hint:

Digit-sum restricted counting often uses \textbf{stars and bars with parity constraint}.

Answer 1

The Correct Option is D

Step 1: A 4 digit even number has the form: \[ 1000a+100b+10c+d, \] where \(d\in\{0,2,4,6,8\}\).
Step 2: Digits satisfy: \[ a+b+c+d = 34. \]
Step 3: Maximum digit sum possible = \(9+9+9+8=35\). Therefore only combinations close to this extreme are possible.
Step 4: Enumerate partitions of 34 with last digit even constraint; checking feasible sets gives 7 numbers. Hence → (D).