Answer to Question #273354 in Statistics and Probability for moha

Question

A JKUAT messenger is asked to deliver 10 out of 16 letters to the head of department’s office and the remaining to the dean’s office. He gets confused and on arrival to the dean’s office delivers 10 letters at random to the office. What is the probability that only 6 of the letters to be delivered to the dean’s office actually arrive there?

Answer 1

number of ways to take 10 letters from total 16:

$n_1=C^{10}_{16}=\frac{16!}{10!6!}=8008$

number of ways to take 6 letters from total 10:

$n_2=C^{6}_{10}=\frac{10!}{4!6!}=210$

probability that only 6 of the letters to be delivered to the dean’s office actually arrive there:

$P=n_2/n_1=210/8008=0.0262$