Question

How many 5 digit numbers greater than 43000 can be formed from the digits {2,3,4,5,6,7}, if repetition of the digits is allowed? A. 8×6⁴ B. 33×6⁴ C. 6⁵ D. 23×6³ E. 8×6³

Answer 1

To find the number of 5-digit numbers greater than 43,000 that can be formed using the digits {2, 3, 4, 5, 6, 7} with repetition allowed, we can break it down into the following cases:

1. For the first digit (the thousands place), it can be 4, 5, 6, or 7 (since it must be greater than 4).

2. For the remaining four digits (the units, hundreds, tens, and ones places), each can be any of the digits {2, 3, 4, 5, 6, 7}.

Now, we can calculate the number of possibilities for each case:

1. For the first digit, there are 4 choices (4, 5, 6, or 7).

2. For the remaining four digits, each has 6 choices (2, 3, 4, 5, 6, or 7), as repetition is allowed.

So, the total number of 5-digit numbers greater than 43,000 that can be formed is:

4 (choices for the first digit) * 6^4 (choices for the remaining four digits) = 4 * 6^4

Now, calculate this value:

4 * 6^4 = 4 * 1,296 = 5,184

So, the correct answer is A. 8×6⁴, which is 4 * 6^4.

Explanation: