Statıstıcs I Deneme Sınavı Sorusu #838219

In how many different ways can the letters in P R O B A B I L I T Y be arranged?


11

55

66

110

11!


Yanıt Açıklaması:

When order is not important, the arrangements of r objects from n distinct objects is called a combination. The number of combinations of size r from a collection of n objects is denoted by C(n,r), and it is given by C(n,r)= P(n,r)/r! = n!/r!(n - r)! when 0≤r≤n.

For P R O B A B I L I T Y there are in total 11 letters but B and I is used twice so they should be counted only once.

r=9, n=11 therefore 11!/9!(11-9)! = (10*11)/2! = 55. The answer is B.

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