How many positive five-digit even integers can be formed

Question

How many positive five-digit even integers can be formed from the digits 2,3,5,7 and 9 in no repeations are allowed?
1
10
16
24
120
Please explain your answer. 
Optional: time you spend on this question

prov · Answer

To make it even, last digit must be 2 only
for the rest, _ _ _ _ 2
all possible = 4*3*2*1 = 24

FN · Answer

what would be the answer if repitition was allowed?

4*4*4*4?

prov · Answer

I'd say 5*5*5*5 because 2 can be included as well

jingy77 · Answer

Im not sure I understand. There are 5 different numbers, what would be the repetitions?

GMAT TIGER · Answer

5 digit integer: a b c d e
e can have only 2 to make the numbers even.
so we can fill only abcd by integers 3, 5, 7, and 9. so they can be filled in 4! (or 24) ways since no repetation is allowed.

if repetation is allowed: abcde = 5x5x5x5x5 = 5^5.

prov · Answer

if no repetition is allowed, given same other conditions, shouldn't it be 5^4 because the last digit must still be 2 only

pmenon · Answer

so the answer to this question is 24.

_ _ _ _ _

in the last spot,we must have 2 to make the number even. in the other four spots, we can put any of the 4 remaining #s, but since repitition is not allowed, we have 4 x 3 x 2 x 1 x 1 = 24

GMAT TIGER · Answer

if repetition is allowed, given same other conditions, = 5^4 because the last digit must be 2 only.
if repetation is allowed (I mean without any condition): abcde = 5x5x5x5x5 = 5^5.

How many positive five-digit even integers can be formed

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards