Advertisements
Advertisements
प्रश्न
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
पर्याय
30
31
32
33
Advertisements
उत्तर
31
\[= 2 \times^5 C_1 + 2 \times {}^5 C_2 +^5 C_5 \]
\[ = 2 \times 5 + 2 \times \frac{5!}{2! 3!} + 1 \]
\[ = 10 + 20 + 1 \]
\[ = 31\]
APPEARS IN
संबंधित प्रश्न
How many chords can be drawn through 21 points on a circle?
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
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.
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?
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
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?
Compute:
(i)\[\frac{30!}{28!}\]
In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?
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 9-digit numbers of different digits can be formed?
How many 3-digit numbers are there, with distinct digits, with each digit odd?
If 8Cr − 7C3 = 7C2, find r.
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
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 (ii) triangles
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
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 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: atmost 3 girls?
If nC12 = nC8 , then n =
If nCr + nCr + 1 = n + 1Cx , then x =
Find the value of 20C16 – 19C16
The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______
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 ______.
How many committee of five persons with a chairperson can be selected from 12 persons.
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 one boy and one girl
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.
Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye 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.
Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is `(11!)/(5!6!) (9!)(9!)`.
To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is 5C3 × 20C9.
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.
A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.
There are ten boys B1, B2, ...., B10 and five girls G1, G2, ...., G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group is ______.
A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is
