There is a 6 digit telephone number with all different digits. If the digit at…
2025
There is a 6 digit telephone number with all different digits. If the digit at extreme right and extreme left are 2 and 5 respectively . How many such telephone numbers are possible ?
- A.
1260
- B.
1680
- C.
2520
- D.
840
Attempted by 461 students.
Show answer & explanation
Correct answer: B
Answer: 1680
Explanation: The telephone number is 6 digits long with all digits different. The leftmost digit is fixed as 5 and the rightmost digit is fixed as 2, so those two digits cannot be used in the middle four positions.
That leaves 10 − 2 = 8 remaining distinct digits (0,1,3,4,6,7,8,9) to fill the four middle places. Since order matters and digits cannot repeat, count permutations of 8 items taken 4 at a time.
Number of ways = 8P4 = 8 × 7 × 6 × 5
Compute: 8 × 7 = 56; 56 × 6 = 336; 336 × 5 = 1680
Therefore the total number of such telephone numbers is 1680.