Advertisements
Advertisements
Question
A letter lock contains 3 rings, each ring containing 5 different letters. Determine the maximum number of false trials that can be made before the lock is opened?
Advertisements
Solution
Since there are 3 rings each containing 5 different letters.
∴ each ring can be adjusted in 5 different ways,
i.e., m = 5, n = 5, p = 5
∴ by the fundamental principle, 3 rings can be arranged in
= m × n × p
= 5 × 5 × 5
= 125 ways
Out of these 125 trials only one trial is successful to open the lock.
Hence, the maximum number of false trials
= 125 − 1
= 124
APPEARS IN
RELATED QUESTIONS
How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
How many two letter words can be formed using letters from the word SPACE, when repetition of letters is allowed?
How many two-letter words can be formed using letters from the word SPACE, when repetition of letters is not allowed?
How many numbers between 100 and 1000 have 4 in the units place?
A Signal is generated from 2 flags by putting one flag above the other. If 4 flags of different colours are available, how many different signals can be generated?
How many two letter words can be formed using letters from the word SPACE, when repetition of letters is allowed?
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are allowed?
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are not allowed?
How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?
In a test, 5 questions are of the form 'state, true or false'. No student has got all answers correct. Also, the answer of every student is different. Find the number of students appeared for the test.
How many four digit numbers will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?
A school has three gates and four staircases from the first floor to the second floor. How many ways does a student have to go from outside the school to his classroom on the second floor?
Select the correct answer from the given alternatives.
A college offers 5 courses in the morning and 3 in the evening. The number of ways a student can select exactly one course, either in the morning or in the evening
Answer the following:
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
There are 3 types of toy car and 2 types of toy train available in a shop. Find the number of ways a baby can buy a toy car and a toy train?
How many two-digit numbers can be formed using 1, 2, 3, 4, 5 without repetition of digits?
A mobile phone has a passcode of 6 distinct digits. What is the maximum number of attempts one makes to retrieve the passcode?
Given four flags of different colours, how many different signals can be generated if each signal requires the use of three flags, one below the other?
Four children are running a race:
In how many ways can the first two places be filled?
Four children are running a race:
In how many different ways could they finish the race?
How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5? if repetition of digits allowed
How many three-digit odd numbers can be formed by using the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is not allowed
Count the total number of ways of answering 6 objective type questions, each question having 4 choices
Find the number of ways of distributing 12 distinct prizes to 10 students?
Find the value of 6!
Find the value of `(12!)/(9! xx 3!)`
Find the value of `(("n" + 3)!)/(("n" + 1)!)`
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 10, r = 3
Choose the correct alternative:
In an examination there are three multiple choice questions and each question has 5 choices. Number of ways in which a student can fail to get all answer correct i
In how many ways can this diagram be coloured subject to the following two conditions?
(i) Each of the smaller triangle is to be painted with one of three colours: red, blue or green.
(ii) No two adjacent regions have the same colour.
Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.
A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing question
Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point
The number of possible outcomes when a coin is tossed 6 times is ______.
The number of different four-digit numbers that can be formed with the digits 2, 3, 4, 7 and using each digit only once is ______.
The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all at a time is ______.
In a steamer there are stalls for 12 animals, and there are horses, cows and calves (not less than 12 each) ready to be shipped. They can be loaded in 312 ways.
