Advertisements
Advertisements
प्रश्न
How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
(a) 6
(b) 20
(c) 60
(d) 120
विकल्प
6
20
60
120
Advertisements
उत्तर
120
\[\text{Number of committes that can be formed} = {}^6 C_3 \times {}^4 C_2 \]
\[ = \frac{6!}{3! 3!} \times \frac{4!}{2! 2!} \]
\[ = \frac{6 \times 5 \times 4}{3 \times 2} \times \frac{4 \times 3}{2} \]
\[ = 120\]
APPEARS IN
संबंधित प्रश्न
If nC8 = nC2, find nC2.
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
How many chords can be drawn through 21 points on a circle?
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?
Compute:
(i)\[\frac{30!}{28!}\]
Prove that
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?
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 odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 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?
A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.
From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
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 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 (i) diagonals
Find the number of ways in which : (a) a selection
Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
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?
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
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
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
Find the value of 80C2
Find the value of 20C16 – 19C16
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?
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is ______.
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, 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 ______.
