CMAT Probability, Combinatorics questions

Given below are two statements :
A number of distinct 8-letter words are possible using the letters of the word SYLLABUS. If a word in chosen at random, then

Statement I: The probability that the word contains the two S's together is $$\frac{1}{4}$$

Statement II : The probability that the word begins and ends with L is $$\frac{1}{28}$$.
In the light of the above statements, choose the correct answer from the options given below

What is the probability of getting a sum of 22 or more when four dice are thrown?

Given below are two statements :
Statement I: The number of ways to pack six copies of the same book into four identical boxes where a box can contain as many as six books, is 9.
Statement II: The minimum number of students needed in a class to guarantee that there are at least six students whose birthday fall in the same month, is 61 .
In the light of the above statements, choose the correct answer from the options given below.

Given below are two statements:
Statement I: Let A and B be two events such that P(A) = 0.6, P(B) = 0.2 and P(AB) = 0.5. Then P(AC BC) = $$\frac{3}{10}$$
Statement II: Let A and B be two events such that P(A) = 0.2, P(B) = 0.4 and P(AUB) = 0.6. The.n P(AB) = $$\frac{3}{10}$$
In the fight of the above statements choose the most appropriate answer from the options given below:

Given below are two statements:
Statement I : A bag captains 10 white and 10 red face masks which are all mixed up. The fewest number of face masks you can take from a bag without looking and be sure to get a pair of the same color is 3.
Statement II: The minimum number of students needed in a class to guarantee that there are at least 6 students whose birthdays fall in the same month, is 61.
In the light of the above statements, choose the most appropriate answer from the option given below:

A bag contains 6 red balls, 11 yellow balls and 5 pink balls. If two balls are drawn at a random from the bag, one after another. What is the probability that the first ball drawn was red and the second ball drawn was yellow in colour?

In a bag there are 15 red balls and 10 green balls. Three balls are selected at random. The probability of selecting 2 red balls and 1 green ball is :

Given below are two statements
Statement I : A committee of 4 can be made out of 5 men and 3 women containing at least one woman in 65 ways.
Statement II : The number of words which can be formed using letters of the word ARRANGE' so that vowels always occupy even place is 36.

In light of the above statements, choose the correct answer from the options given below

How many ten-digit numbers can be formed using all the digits of 2435753228 such that odd digits appear only in even places?

Match List I with List II.
Let A and B be events with $$P(A)=\frac{2}{3}, P(B)=\frac{1}{2}$$ and $$P(A\cap B)=\frac{1}{3}$$

(Here c stands for complement)
Choose the correct answer from the options given below:

During the next year, the probability that a Company A releases a mobile is 0.7. The probability that mobile is a success. given that it is released by the Company is 0.8. The probability that a mobile is a success and released by a Company B is 0.28. A mobile released by either Company A or Company B during the next one year is a success. Find the probability that it is released by Company A.

In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?

Brother and sister both appear for an interview. The probability of the selection of brother is $$\frac{1}{8}$$ while the probability of rejection of sister is $$\frac{4}{5}$$ What is the probability that only one of them is selected ?

There are six teachers. Out of them, two teach physics, other two teach Chemistry and the rest two teach Mathematics. They have to stand in a row such that Physics, Chemistry and Mathematics teachers are always in a set. The numberof ways in which they can do, is :

In how many different ways, can the letters of the words EXTRA be arranged so that the vowels are never together ?

There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or person 2. Task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done ?

What is the probability of drawing a king or a heart from a deck of cards ?

In a simultaneous throw of a pair of dice, find the probability of getting a total of 9 or more.

A management institute has 6 senior professors and 4 junior professors, 3 professors are selected at random for a government project. The probability that at least one of the junior professors would get selected is :

What is the probability of getting a ‘nine’ or ‘ten’ on a single throw of two dice?