Permutation and Combination Moderate Questions and Answers

Permutation and Combination

How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter ?

Total number of password using all alphabets -Total
number of password using no symmetric alphabets

Correct Option: C

Total number of password using all alphabets -Total
number of password using no symmetric alphabets
= (26 x 25 x 24 ) - (15 x 14 x 13 )
= 12870

A question paper had 10 questions. Each question could only be answered as True (T) or false (F). Each candidate answered all the questions. Yet, no two candidate wrote the answers in an identical sequence. How many different sequences of answers are possible ?

Each question can be answered in 2 ways.

Correct Option: D

Each question can be answered in 2 ways.
∴ 10 question can be answered = 2¹⁰ = 1024 ways

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 ?

Maximum number of such different groups = ABC , ABD, ABE, BCE, BDE, CEA, DEA = 7

Correct Option: C

Maximum number of such different groups = ABC , ABD, ABE, BCE, BDE, CEA, DEA = 7

In a question paper, there are four multiple choice type question. Each question has five choices with only one choice for its correct answer. What is the total number of ways in which a candidate will not get all the four answers correct ?

No of multiple choice type questions = 4
Total number of ways = 5 x 5 x 5 x 5 = 625
Number of correct answer = 1

Correct Option: C

No of multiple choice type questions = 4
Total number of ways = 5 x 5 x 5 x 5 = 625
Number of correct answer = 1
Number of false answers = 625 - 1 = 624

In how many difference ways can six players be arranged in a line such that two of them, Abhinav and Manjesh are never together ?

As, there are six players, so total ways in which they can be arranged = 6 ! ways

Correct Option: C

As, there are six players, so total ways in which they can be arranged = 6 ! ways
Also, two particular players,are never together.
∴ Required ways = 6!/2! = 360