Advertisements
Advertisements
Question
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
Solution
From 4 officers and 8 jawans, 6 need to be chosen. Out of them, 1 is an officer.
Required number of ways =\[{}^4 C_1 \times {}^8 C_5 = 4 \times \frac{8!}{5! 3!} = 4 \times \frac{8 \times 7 \times 6 \times 5!}{5! \times 6} = 224\]
APPEARS IN
RELATED QUESTIONS
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.
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?
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?
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?
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
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?
From Goa to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there?
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
Twelve students complete in a race. In how many ways first three prizes be given?
How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?
How many 9-digit numbers of different digits can be formed?
Evaluate the following:
35C35
f 24Cx = 24C2x + 3, find x.
If nC4 , nC5 and nC6 are in A.P., then find n.
If 16Cr = 16Cr + 2, find rC4.
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
How many different selections of 4 books can be made from 10 different books, if
two particular books are always 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?
A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?
Find the number of (ii) triangles
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.
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
If 20Cr = 20Cr−10, then 18Cr is equal to
If 20Cr = 20Cr + 4 , then rC3 is equal to
If nC12 = nC8 , then n =
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
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
There are 8 doctors and 4 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.
Find the value of 80C2
Answer the following:
A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they can be of any colour
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they must all be of the same colour.
15C8 + 15C9 – 15C6 – 15C7 = ______.
The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together 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.
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.
