Question

nia has number cards for 2,3,8,9, and 5. What are all the different ways Nia can arrange the cards to show only even numbers with the 2 in the ten thousands place?

Answer 1

Given that only an even number is allowed for the ten thousand place, there are only 2 even numbers in the number card, hence, there are 2 ways of arranging the ten thousand place, the other 4 places can be arranged in 4! = 24 ways.

Therefore, the number of different ways Nia can arrange the cards to show only even numbers in the ten thousands place is given by 2 x 24 = 48 ways.

Answer 2

The correct answer is:

6 ways.

Explanation:

The two must be in the ten-thousands place. The number must be an even number; the only even digit left is 8, so this must be in the 1s place. Treating these as a "group," there is 1 way to arrange these two digits in that order.

This leaves us the remaining 3 digits to arrange in the middle. There are 3!=3(2)(1)=6 ways to arrange those 3 digits. This gives us a total of 6(1) = 6 ways to arrange these.