Question

Skip likes to use clichés. If Skip plans on living 60 years (ignore leap years) how many clichés does he need to have in order not to use the same three on any day of those 60 years?

Answer 1

Number of sets of cliches needed = Number of days in 60 years

= 60x365

= 21900

Let the number of cliches needed to make 21900 sets of cliches be n

Number of ways to make a set of r items from a set of n items, nCr = n!/(r! x (n-r)!)

Here. number of items in the set, r = 3

We know that the number of sets = 21900

So, nC₃ = 21900

n!/(3! x (n-3)!) = 21900

n x (n - 1) x (n - 2) / 3! = 21900

n x (n-1) x (n - 2) = 131400

n (n² - 3n + 2) = 131400

n³ - 3n² + 2n - 131400 = 0

n = 51.85

So, number of cliches required = 52