How many different numbers greater than 60000 can be formed with the d

1.	How many different numbers greater than 60000 can be formed with the digits 0, 2, 2, 6, 8? (a) 144 (b) 48 (c) 24 (d) 288
Answer» (c) 24 Numbers greater than 60000 will have either 6 or 8 in the TTh place and will consist of 5-digits. If the digit 6 occupies the TTh place, the remaining 4 places can be occupied in \(\frac{4!}{2!}\) ways. (∵ There are two 2’s) Number of numbers beginning with 6 = \(\frac{4!}{2!}\) = 12 Similarly, number of numbers beginning with 8 = \(\frac{4!}{2!}\) = 12 ∴ Number of different numbers greater than 60000 formed with digits 0, 2, 2, 6, 8 = 12 + 12 = 24.

How many different numbers greater than 60000 can be formed with the digits 0, 2, 2, 6, 8? (a) 144 (b) 48 (c) 24 (d) 288

Answer»

(c) 24

Numbers greater than 60000 will have either 6 or 8 in the TTh place and will consist of 5-digits.

If the digit 6 occupies the TTh place, the remaining 4 places can be occupied in \(\frac{4!}{2!}\) ways. (∵ There are two 2’s)

Number of numbers beginning with 6 = \(\frac{4!}{2!}\) = 12

Similarly, number of numbers beginning with 8 = \(\frac{4!}{2!}\) = 12

∴ Number of different numbers greater than 60000 formed with digits 0, 2, 2, 6, 8

= 12 + 12 = 24.