# Problem of the Day: 2/10/13

In a standard deck of 52 cards, what is the probability that the first three cards drawn without replacement will be of different suits? Express your answer to the nearest whole percent.

Solution to yesterday’s problem:

The number of bacterial cells in the population can be expressed as the number of original cells x times two for each hour that the population doubles. We can write this as

$P=x\times 2^n$

where n is the number of hours and P is the population size. In the problem, we are given 7 hours and 38,400 cells. Substituting these into the equation:

$38400=x\times 2^7$

Simplifying the exponent,

$38400=128x$

Dividing,

$x=300$

We conclude that there were 300 cells in the original sample.