Question

Irving can I remember the correct order of the five digits on his ID number he does remember that the ID number contains the digits 1.4,3,7,6 what is the probability that the first three digits of Irvings ID number will be odd numbers

Answer 1

Answer: $\frac{27}{125}$

Step-by-step explanation:

Here the total numbers are 1,  4,  3,  7,  6

Since the total number of possible arrangement = $5\times 5 \times5 \times 5 \times 5=5^5$

The total number of the odd numbers in the given numbers = 3

Thus the possible arrangement that the first three digits will be odd numbers = $3\times 3\times 3\times 5\times 5=3^3\times 5^2$

Thus, the probability that the first three digits of Irvings ID number will be odd numbers = the possible arrangement that the first three digits will be odd numbers / total possible arrangement =  $\frac{3^3\times 5^2}{5^5} = \frac{3^2}{5^{5-2}}$

= $\frac{3^3}{5^3} = \frac{27}{125}$