Love those arbitrary restricted range

Probability Level 2

How many positive integers less than 500 exist with their units digit a 0, 2 or 9?

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120 150 179 149

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Sandeep Bhardwaj
Sep 18, 2014

Numbers that can be used at unit digit's place= 3 (i.e. 0,2 and 9 )

Numbers that can be used at ten's digit place= 10

Numbers that can be used at hundred's digit place=5 (i.e. 0,1,2,3,4 )

So total numbers $= 3 \times 10 \times 5$ =150

But 000 is also included in those numbers, but not being a positive integer, it must be excluded.

So required positive integers $=\boxed{149}$

Yep you should be careful in removing that 000

Anand Raj - 6 years, 6 months ago

I noticed that at the last minute and saved myself from an epic failure. :P

Sudeshna Pontula - 6 years, 3 months ago

500 x 3/10 = 150 // only 3/10 out of 500 integers (000-499) fulfill the requirement.

150 - 1 =149 // 000 is not included.

BK Lim - 6 years, 3 months ago

Ahmed Hussein
Oct 21, 2014

simply, every 100 numbers there is 10 numbers whereas their units are 0,2 or 9 , but the confusion is that the number 500 is not included in the interval mentioned in the problem, so that 500 cannot be considered as a number where its units is 0,Because of the condition that the numbers must be LESS THAN 500.

Brock Brown
Dec 27, 2014

count = 0
for i in xrange(1,500):
    for digit in '029':
        if str(i).endswith(digit):
            count += 1
            break
print count

Love those arbitrary restricted range

Try more combinatorics problems.

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