Seven people leave their bags outside at temple and returning after worshiping picked one bag each at random. In how many ways at least one and at most three of them get their correct bags?

A bag contains twelve pairs of socks and four socks are picked up at random. The probability that there is at least one pair is equal to -

There are six periods in each working day of the school. In how many ways can one arrange 5 subjects such that each subject is allowed at least one period?

A question paper contains 12 questions divided into three parts.Parts A contains 6 questions while B and C contains 3 questions each.A candidate is required to attempt 6 questions selecting at least two from part A and atleast one from each of the parts B and C.In how many ways can the candidate select 6 questions?

A question paper contains 12 questions , divided into three parts . Part A contains 6 questions parts B and C contain 3 questions each A candidate is required to attempt 6 questions , selecting at least 3 questions from part A and at least one from each of the parts B and C In how many ways can the candidate select his 6 questions ?

In how many ways 14 identical toys be distributed among three boys so that each one gets atleast one toy and no two boys get equal no of toys ?

There are 3 sections in a question paper each containing 5 questions. A candidate has to solve only 5 questions, choosing at least one question from each section. In how many ways can he make his choice ?

In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

A question paper on mathematics consists of 12 questions divided into 3 parts A, B and C, each containing 4 questions. In how many ways can an examinee answer 5 questions selecting at least one from each part.

Each of the two identical bags contain 5 white and 5 red balls. One ball is transferred at random without notice from the second bag to the first bag. Then one ball is drawn from the first bag. Find the probability that the ball drawn is a red ball.

A person draws out two balls successively from a bag containing 6 red and 4 white balls. The probability that at least one of them will be red is