GATE Overflow | Mathematics | Test 1 | Question: 24

Question

Rama wrote 5 different letters. He prepared 5 different envelopes for the 5 letters. If he randomly distributes the 5 letters to the 5 envelops what is the probability that each letter gets into correct envelope ?

• A. 1/2       
• B. 1/5   
• C. 1/60          
• D. 1/120

Answer 1

Total combination are 5! for the 5 letters to be placed.
Favourable case(s) = 1

Probability = 1/120

Answer 2

Let the letters be: L1, L2, L3, L4, L5.

Let the Envelopes be: E1, E2, E3, E4, E5.

__ __ __ __ __ Let each position represent an envelope.

Correct matching — 1.

All possible matchings: 5! = 120.

So, 1/120.

Option D