Advertisements
Advertisements
प्रश्न
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. He can choose the seven questions in 650 ways.
विकल्प
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
The candidate may attempt in following manner
| Group A | 2 | 3 | 4 | 5 |
| Group B | 5 | 4 | 3 | 2 |
So, the number of attempts of 7 questions
= 6C2 × 6C5 + 6C3 × 6C4 + 6C4 × 6C3 + 6C5 × 6C2
= 2[6C2 × 6C5 + 6C3 × 6C4]
= 2 [15 × 6 + 20 × 15]
= 2[90 + 300]
= 2 × 390
= 780.
APPEARS IN
संबंधित प्रश्न
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?
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?
A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?
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?
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 three-digit numbers are there?
How many three-digit odd numbers are there?
Evaluate the following:
14C3
Evaluate the following:
n + 1Cn
If nC4 = nC6, find 12Cn.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
If n +2C8 : n − 2P4 = 57 : 16, find n.
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
include 2 particular players?
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular student is included.
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?
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
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.
Find the number of diagonals of (ii) a polygon of 16 sides.
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
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?
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.
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 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?
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?
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 43Cr − 6 = 43C3r + 1 , then the value of r is
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
Find the value of 15C4 + 15C5
A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?
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
The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them 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 ______.
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 ______.
The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.
