Advertisements
Advertisements
Question
A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?
Advertisements
Solution
Number of ways of marking each of the ring = 10 different letters
∴ Total number of ways of marking any letter on these three rings = 10\[\times\]10\[\times\]10 = 1000 Out of these 1000 combinations of the lock, 1 combination will be successful.
∴ Total number of unsuccessful attempts = 1000 \[-\]1 = 999
APPEARS IN
RELATED QUESTIONS
How many chords can be drawn through 21 points on a circle?
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?
It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
From Goa to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there?
Twelve students complete in a race. In how many ways first three prizes be given?
How many 9-digit numbers of different digits can be formed?
Evaluate the following:
12C10
If nC12 = nC5, find the value of n.
If 15C3r = 15Cr + 3, find r.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
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. In how many ways can he choose the 7 questions?
In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines
A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
If 15C3r = 15Cr + 3 , then r is equal to
If C (n, 12) = C (n, 8), then C (22, n) is equal to
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
Find the value of 20C16 – 19C16
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they must all be of the same colour.
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least three girls.
If nC12 = nC8, then n is equal to ______.
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.
Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ______.
If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.
