Saved Bookmarks
| 1. |
How many numbers greater than a million can be formed with the digits 2, 3, 0, 3, 4, 2, 3? |
|
Answer» A million is a 7-digit number. So any number greater than 1 million will contain all the seven digits. Since the digit 2 occurs twice and digit 3 occurs thrice and the rest are different, therefore, number of possible numbers which can be formed with the given seven digits = \(\frac{7!}{(2!)(3!)}=420.\) These possible numbers include those which have 0 at the millions place. Keeping 0 fixed at the millions place, the remaining 6 digits out of which 2 occurs twice, 3 occurs thrice and the rest are different can be arranged in = \(\frac{6!}{(2!)(3!)}\) = 60. ways. ∴ Number of numbers greater than 1 million made from the given digits = 420 – 60 = 360. |
|