data analysis question help please

[ben.chantana]

How many 3-digit positive integers are odd and do not contain the digit 5?

Thank you so much!

[garima_aries01]

How many 3-digit positive integers are odd and do not contain the digit 5?

Thank you so much!

A B C

digit C -units place:
1st digit from right(unit place -C) should be odd for the number to be odd :
1,3,5,7,9

But the number should not contain 5 so the C can be 1,3,7,9
=> unit place C can be occupied in 4 ways

digit B - tens place
tens place can be any digit except 5 . So it can be one of the digits - 0,1,2,3,4,6,7,8,9
Tens place can be occupied in 9 ways

digit A - hundreds place
hundreds place can be occupied by any digit except 0 and 5 because zero at hundreds place will make the number two digit number.
So the digits can be 1,2,3,4,6,7,8,9
hundreds place can be occupied in 8 ways.

8 ways x 9 ways x 4 ways= 288

[tommywallach]

Hey Ben,

Garima's answer totally nailed it. This is a COMBINATORICS question, and we solve that with the slot method:

1) Find # of slots (places you can make a decision)

2) Fill in each slot with the # of choices at each decision point

3) Multiply across; if the order doesn't matter, also divide by the # of slots factorial

In this case, the order absolutely matters (the whole question is about how many ways you can order the digits, meaning 1237 is different from 7321). That means you just have to work out the number of choices you have for each digit place. Garima's explanation of that is spot on.

Let me know if you have further questions!

-t

[ben.chantana]

thank you! This is much more simple than I thought!

[tommywallach]

Glad to help!

-t