Question

The answer I got was wrong, what is the correct answer and show work

19. (a) How many 5-digit nuhabers have all theîr digits different? 12 (b) How many of these 5-digit numbers are odd-numbers? [3] (c) How many of them are even? 13]

Answer 1

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19.

a. 1st digit number can't be a 0. if it is, then it will become a 4-digit number.

Also, in the second blank you can put 0, so you are missing that and using 8 instead of 9
= 9*9*8*7*6
= 27,216

b. how many are odd ?
you place an odd in 5 ways in the last digit ( 1,3,5,7,9)
_ _ _ _ odd

in the first blank you can put 8 numbers ( 10-1odd number - zero)

In the second blank you can put 8

xxxx(1/3/5/7/9)
Hence, 8*8*7*6*5 = 13440

c.

last digit is 0: xxxx1 = 9*8*7*6*1 = 3,024
last digit is 2,4,6 or 8: xxxx(24/6/8) = 8*8*7*6*4 = 10,752

total ways possible = 3024+10752 = 13772