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
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.
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:
(i) exactly 3 girls?
(ii) atleast 3 girls?
(iii) atmost 3 girls?
Compute:
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
In how many ways can an examinee answer a set of ten true/false type questions?
Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?
How many three-digit numbers are there?
How many 3-digit numbers are there, with distinct digits, with each digit odd?
How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?
Evaluate the following:
35C35
If 8Cr − 7C3 = 7C2, find r.
If α = mC2, then find the value of αC2.
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?
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?
How many triangles can be obtained by joining 12 points, five of which are collinear?
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(iii) at least 3 girls?
Find the number of (i) diagonals
Determine the number of 5 cards combinations out of a deck of 52 cards if at least one of the 5 cards has to be a king?
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
If C (n, 12) = C (n, 8), then C (22, n) is equal to
There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
Find the value of 15C4
If α = mC2, then αC2 is equal to.
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.
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.
A convex polygon has 44 diagonals. Find the number of its sides.
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 no girls
The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is ______.
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
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 |
