Advertisements
Advertisements
Question
Find the number of (ii) triangles
Advertisements
Solution
(ii) Number of triangles (i.e. 3 sides are to be selected) = \[{}^{10} C_3 = \frac{10}{3} \times \frac{9}{2} \times \frac{8}{1} = 120\]
APPEARS IN
RELATED QUESTIONS
How many chords can be drawn through 21 points on a circle?
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?
A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
How many three-digit numbers are there with no digit repeated?
How many different five-digit number licence plates can be made if
first digit cannot be zero and the repetition of digits is not allowed,
A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.
Evaluate the following:
35C35
Evaluate the following:
n + 1Cn
If nC12 = nC5, find the value of n.
If n +2C8 : n − 2P4 = 57 : 16, find n.
If 16Cr = 16Cr + 2, find rC4.
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: exactly 3 girls?
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
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
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
If 15C3r = 15Cr + 3 , then r is equal to
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
Find the value of 80C2
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l2, k points on l3. The maximum number of triangles formed with vertices at these points are ______.
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.
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 ______.
A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.
A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ______.
There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:
| C1 | C2 |
| (a) One book of each subject; | (i) 3968 |
| (b) At least one book of each subject: | (ii) 60 |
| (c) At least one book of English: | (iii) 3255 |
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.
All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is ______.
There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.
