Question

A five digit number is chosen at random what is the probability there are exactly 2 zeros

Answer 1

2/5 is the probability of getting 2 zeroes...

Answer 2

Answer:

0.0486

Step-by-step explanation:

# 5 digit numbers = 10⁵ - 10⁴ = 9 × 10⁴

Now count 5 digit numbers with exactly 2 zeros.

There are 4 places where the 2 zeros can go (the first digit is not 0).  So there are $\displaystyle\binom42$=6 ways to select where they go.  Then each of the remaining 5 digits can be any of the 9 nonzero digits, so there are 9³ ways of selecting them.  In total then:

# 5 digit numbers with exactly 2 zeros = 6 × 9³

Therefore:

P(getting a number with exactly 2 zeros)

= (# 5 digit numbers with exactly 2 zeros) / (# 5 digit numbers)

= ( 6 × 9³ ) / ( 9 × 10⁴ )

= ( 6 × 9² ) / 10⁴

= ( 6 × 81 ) / 10⁴

= 486 / 10⁴

= 0.0486