Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given that question number 1 and 2 are compulsory
∴ The remaining questions are 5 – 2 = 3
Total number of questions to be attempted = 4 questions 1 and 2 are compulsory
So only 2 questions are to be done out of 3 questions
Therefore number of ways = 3C2
= 3C3–2
= 3 ......`[∴ ""^nC_r = ""^nC_(n - r)]`
Hence, the required number of ways = 3.
APPEARS IN
RELATED QUESTIONS
How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?
There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?
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,
In how many ways can six persons be seated in a row?
How many different numbers of six digits each can be formed from the digits 4, 5, 6, 7, 8, 9 when repetition of digits is not allowed?
Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?
Evaluate the following:
14C3
Evaluate the following:
35C35
If nC4 = nC6, find 12Cn.
If 8Cr − 7C3 = 7C2, find r.
If nC4 , nC5 and nC6 are in A.P., then find n.
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
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?
Find the number of diagonals of , 1.a hexagon
In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?
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 (i) no girl?
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can the selection be made?
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
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 parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is
The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is
If n + 1C3 = 2 · nC2 , then n =
Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.
There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?
Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections.
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
In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 2 particular players?
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 ______.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is ______.
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` 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 ______.
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.
