SNAP Probability, Combinatorics questions

ABC Paints Ltd. is planning to create different combination of dyes. The research team has decided they will be using five different green dyes, three different red dyes and four different blue dyes. How many combinations of dyes can be created by ABC Paints Ltd., by including at least one blue and one green dye?

Sonal and Meenal appear in an interview for same post having two vacancies. If $$\frac{1}{7}$$ is Sonal's probability of selection and $$\frac{1}{5}$$ is Meenal's probability of selection then what is the probability that only one of them is selected?

Big Bang Theory cast wishes to find out the number of ways in which the word ASTRONAUT can be scrambled. They find that the number of ways in which it can be put in an unscrambling puzzle is?

How many different words can be formed with the word CUSTOM with a condition that the word should begin with M?

Assume that all words have 6 distinct letters.

The number of ways that 5 Marathi, 3 English and 3 Tamil books be arranged if the books of each language are to be kept together is

How many words each of two vowels and three consonants can be formed from the letters of the word "UNIVERSAL" ?

Sonali can solve 70% of the problems in a competitive exam and Nirali can solve only 60% in the same exam. What is the probability that at least one of them will solve a problem, provided selection of questions is done randomly from the same exam ?

A person has a bag which contains 9 bulbs out of which 2 are fused and cannot be used to lighten the room. Two bulbs are selected at random. What is the probability that all the two bulbs chosen can be used to lighten the room ?

There are nine humans in a ship, each human has nine cages and each cage has nine huge lions and each lion has nine cubs. How many legs are there in the ship ? (Human have two legs, lions have four legs, cubs have four legs.)

How many different letter arrangements can be made from the letter of the word EXTRA in such a way that the vowels are always together?

In a given race the odds in favour of three horses A, B, C are 1:3; 1:4; 1:5 respectively. Assuming that dead heat is impossible the probability that one of them wins is

A bag contains 5 white and 3 black balls, and 4 are successively drawn out and not replaced. What’s the chance of getting different colours alternatively?

A bag contains 100 tickets numbered 1, 2, 3, .... 100. If a ticket is drawn out of it at random, what is the probability that the ticket drawn has the digit 2 appearing on it?

There are five boys and three girls who are sitting together to discuss a management problem at a round table. In how many ways can they sit around the table so that no two girls are together?

The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a meeting consisting of 8 ladies and 7 gentlemen, if Mrs. X refuses to serve in a committee if Mr. Y is its member, is

A family consists of a grandfather, 5 sons and daughters and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. The number of ways in which the family can be made to sit is

At a college football game, $$\frac{4}{5}$$ of the seats in the lower deck of the stadium were sold. If $$\frac{1}{4}$$ of all the seating in the stadium is located in the lower deck, and if $$\frac{2}{3}$$ of all the seats in the stadium were sold, then what fraction of the unsold seats in the stadium was in the lower deck?

The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays, is:

A bag contains 5 white and 3 black balls; another bag contains 4 white and 5 black balls. From any one of these bags a single draw of two balls is made. Find the probability that one of them would be white and another black ball.

If $$^nC_x = 56$$ and $$^nP_x = 336$$, then Find n and x?