Q. 325.0( 1 Vote )
One mapping is selected at random from all the mappings of the set A = {1, 2, 3, ….., n) into itself. The probability that the mapping selected is one to one is
A. 
B. 
C. 
D. none of these
Answer :
We know that the no of mapping from a set A to same set containing n elements = nn
As each element have n options to be mapped with n elements.
For mapping selected to be one to one, for first element we have n options ,for second we have n-1 options an so on…
∴ total such mappings = n × (n-1)× (n-2)× … = n!
∴ P(mapping is one to one) = 
Our answer matches with option (c)
∴ Option (c) is the only correct choice
Rate this question :
A natural number is chosen at random from amongst first 500. What is the probability that the number so chosen is divisible by 3 or 5?
RD Sharma - MathematicsIn a single throw of two dice, find the probability that neither a doublet nor a total of 9 will appear.
RD Sharma - MathematicsOne of the two events must happen. Given that the chance of one is two-third of the other, find the odds in favour of the other.
RD Sharma - MathematicsA card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.
RD Sharma - MathematicsOne of the two events must occur. If the chance of one is 2/3 of the other, then odds in favour of the other are
RD Sharma - MathematicsThe probability that a person will travel by plane is 3/5 and that he will travel by train is 1/4. What is the probability that he (she) will travel by plane or train?
RD Sharma - MathematicsIf the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is
RD Sharma - Mathematics