Question

# Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct .A. 60000B. 65000C. 70000D. 75000

Out of 26 alphabets two distinct letters can be chosen in $^{26}{P_2}$ ways.
Combined with letters there are $^{26}{P_2} \times 100 = \dfrac{{26!}}{{\left( {26 - 2} \right)!}} \times 1000 = 26 \times 25 \times 1000 = 65000$ ways to choose the vehicle numbers.
(since $^n{P_r} = \dfrac{{n!}}{{\left( {n - r} \right)!}}$)