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How many friends must you have to guarantee that at least five of them will have birthday in the same month?
1 Answer
written 2.6 years ago by |
Extended pigeonhole principle.
Let "n" be the number of pigeon and "m" be the number of pigeonholes and
If (m < < n) i.e. number of pigeonholes are less than the number of pigeons then extended pigeonhole principle is applicable
According to extended pigeonhole principle one pigeonhole must contains at-least
[$\frac {n-1}{m} + 1$] pigeons.
Here Number of pigeons = n = ?
No. of pigeonholes = m = 12 (months)
$\therefore$ $[\frac{n-1}{m}] + 1 = 5$
$[\frac{n-12}{m}] + 1 = 5$
n - 1 = 48
n = 49 [ No. of pigeons]
$\therefore$ 49 friends should be their to guarantee that at-least five of them must have birthday in a same month of year