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ISI MStat 2018 PSA Problem 13 | Probability of functions

This is a beautiful problem from ISI MStat 2018 PSA problem 13 based on probability of functions. We provide sequential hints so that you can try .

Probability - ISI MStat Year 2018 PSA Problem 13

Consider the set of all functions from to where If a function is chosen from this set at random, what is the probability that it will be strictly increasing?

Key Concepts

combination

Check the Answer

Answer: is

ISI MStat 2018 PSA Problem 13

A First Course in Probability by Sheldon Ross

Try with Hints

What is the total number of functions from to where (n>m)

You have to choose numbers among and assign it to the For each element of , there are options from . Hence number of functions .

The number of ways to select Select elements among is the same as the number of strictly ascending subsequences of length m taken from 1, 2, 3, ..., n, which is the same as the number of subsets of size m taken from {1,2,3,…,n}, which is .

Hence the probability that it will be strictly increasing

This is a beautiful problem from ISI MStat 2018 PSA problem 13 based on probability of functions. We provide sequential hints so that you can try .

Probability - ISI MStat Year 2018 PSA Problem 13

Consider the set of all functions from to where If a function is chosen from this set at random, what is the probability that it will be strictly increasing?

Key Concepts

combination

Check the Answer

Answer: is

ISI MStat 2018 PSA Problem 13

A First Course in Probability by Sheldon Ross

Try with Hints

What is the total number of functions from to where (n>m)

You have to choose numbers among and assign it to the For each element of , there are options from . Hence number of functions .

The number of ways to select Select elements among is the same as the number of strictly ascending subsequences of length m taken from 1, 2, 3, ..., n, which is the same as the number of subsets of size m taken from {1,2,3,…,n}, which is .

Hence the probability that it will be strictly increasing