As Permutation Questions

[exquisite_mh93]

Q1: A typist has five letters and five addressed envelopes. In how many different ways can the letters be place in each envelope without getting every letter in the right envelope? If the letters are placed in the envelopes at random what is the probability that each letter is in its correct envelope?




Q2: How many different numbers can be formed by taking one, two, three and four digits from the digits 1, 2, 7 and 8, if repetitions are not allowed?

One of these numbers is chosen at random. What is the probability that it is greater than 200?

 

[minigilani]

Ans:
1.
(i) 5P5 - 1 or 5! - 1
there are a total of 5P5, or 5! ways the letters can be arranged in the envelopes.. only one way is correct, subtract the one correct possibilities from the total possibilities, and you are left with the number of wrong possbilities..
(ii) 1/5P5 or 1/5!
there is only one correct way to arrange the letters, and 5!, or 5P5, possible ways to arrange the letters..
the general formula for probability is required outcome/total outcomes.

i'll answer the second question later, i gtg ..

 

[minigilani]

2.
(i) 4P1 + 4P2 + 4P3 + 4P4
selection and arrangement of 1 number from 4 is 4P2, of 2 numbers from 4 is 4P2, of 3 is 4P3, and 4 is 4P4..

(ii) {(4P1 + 4P2 + 4P3 + 4P4) - (4P1 + 4P2 -3P2)} / (4P1 + 4P2 + 4P3 + 4P4)
(total number of arrangements) - (number of arrangements less than 200) / (total number of arrangements)
.
I am good .. (H) .. bye!

 

[exquisite_mh93]

You are indeed good!!! thanks a bunch!!!