Advertisements
Advertisements
Question
How many committee of five persons with a chairperson can be selected from 12 persons.
Advertisements
Solution
Total number of Persons = 12
Number of persons to be selected = 5
Out of 5, there is a chairperson
∴ Number of ways of selecting a chairperson = 12C1 = 12
Number of ways of selecting other 4 numbers out of remaining 11 persons = 11C4
∴ Total number of ways = 12C1 × 11C4
= `12 xx (11*10*9*8)/(4*3*2*1)`
= 12 × 330
= 3960
Hence, the required number of ways = 3960.
APPEARS IN
RELATED QUESTIONS
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
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.
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
Compute:
L.C.M. (6!, 7!, 8!)
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
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 different five-digit number licence plates can be made if
the first-digit cannot be zero, but the repetition of digits is allowed?
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?
How many odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?
How many 3-digit numbers are there, with distinct digits, with each digit odd?
How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 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?
If nC12 = nC5, find the value of n.
If n +2C8 : n − 2P4 = 57 : 16, find n.
If 16Cr = 16Cr + 2, find rC4.
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?
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?
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
If 15C3r = 15Cr + 3 , then r is equal to
Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is
If 43Cr − 6 = 43C3r + 1 , then the value of r is
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
Find the value of 80C2
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 ______
A student has to answer 10 questions, choosing atleast 4 from each of Parts A and B. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions?
If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?
In how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?
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
If nC12 = nC8, then n is equal to ______.
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 ______.
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 ______.
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 ______.
