JEE Main 2021 (Online) 26th August Morning ShiftQuestion 1
The number of three-digit even numbers, formed by the digits $0,1,3,4,6,7$ if the repetition of digits is not allowed, is $\_\_\_\_\_\_$ .
Permutation and Combination
Answer$52$
Solution
Formulas used. (1) Fill places one by one, first digit $\ne0$Step 1 - Last digit 0. First: 5 ways, middle: 4 ways. $20$. Step 2 - Last digit 4 or 6. First digit: not 0, not the last: $4$ ways. Middle: any of the 4 left (0 allowed): $4$. $2\cdot4\cdot4=32$. Step 3 - Total. $20+32=52$. Answer: 52