Permutations & Combinations Mcqs

Q.  The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is_________?

a. (6!)2
b. 6! * ⁷P₆
c. 2(6!)
d. 6! * 7


ANSWER: See Answer
 
We can initially arrange the six boys in 6! ways.

Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways = 6! * ⁷P₆
MCQs:  A student has to opt for 2 subjects out of 5 subjects for a course. Namely commerce, economics, statistics, mathematics 1 and Mathematics 2, Mathematics 2 can be offered only if mathematics 1 has also opted. The number of different combinations of two subjects which can be opted is_________?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  2 men and 1 woman board a bus of which 5 seats are vacant, one of these 5 seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies, In how many different ways can the five seats be occupied by these passengers?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  Three flags each of different colours are available for a military exercise, Using these flags different codes can be generated by waving I. Single flag of different colours II. Any two flags in a different sequence of colours. III. three flags in a different sequence of colours. The maximum number of codes that can be generated is.
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  Three dice (each having six faces with each face having one number from 1 or 6) are ralled. What is the number of possible outcomes such that atleast one dice shows the number 2?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  A mixed doubles tennis game is to be played two teams(each consists of one male and one female) There are four married couples. No team is to consist a husband and his wife. What is the maximum number of games that can be played?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  In a question paper, there are four multiple choice type questions, each question has five choices with only one choice for it’s correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  In how many different ways can six players be arranged in a line such that two of them, Asim and Raheem are never together?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  Groups each containing 3 boys are to be formed out of 5 boys. A, B, C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  A question paper had 10 questions. Each question could only be answered as true(T) of False(F). Each candidate answered all the questions, Yet no two candidates wrote the answers in an identical sequence. How many different sequences of answers are possible?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  Find the number of ways of arranging the letters of the word “MATERIAL” such that all the vowels in the word are to come together?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  The number of new words that can be formed by rearranging the letters of the word ‘ALIVE’ is__________?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  In how many ways can live boys and three girls sit in a row such that all boys sit together?
Category: Mathematics Quizzes,   Published by: T-Code Scripts
MCQs:  Find the least square number which is divisible by 10, 12, 15 and 18?
Category: Mathematics Quizzes,   Published by: T-Code Scripts