numbers 0, 1,2,3,4,5 make an odd 4 -digit number without repetitions

Question

Can someone please help?? I Got stuck and I have a test soon!!

Answer 1

to calculate the number of ways to arrange 4 numbers out of 6 use the formula for a permutation without repetitions.

 

P(n,r) = n!/(n-r)!

since we are arranging a 4 digit sequence out of 6 numbers we have:

 

P(6,4) = 6!/(6-4)!

P(6,4) = 720/2

P(6,4) = 360 possible sequences

 

since 1/2 of the original numbers are odd, 1/2 of the 360 sequences must also be odd

so you are left with

 

P(6,4) = 360/2 

P(6,4) = 180    odd sequences

Answer 2

0, 1,2,3,4,5 make an odd 4 -digit number without repetitions

 

To be odd it must end in either 1, 3, or 5

 

2341

3451

3021

1203

1205

1245

.

.

.

and so forth