Advertisements
Advertisements
प्रश्न
Twelve students complete in a race. In how many ways first three prizes be given?
Advertisements
उत्तर
Number of competitors in the race = 12
Number of competitors who can come first in the race = 12
Number of competitors who can come second in the race = 11 (as one competitor has already come first in the race)
Number of competitors who can come third in the race = 10
∴ Total number of ways of awarding the first three prizes = 12\[\times\]11\[\times\]10 = 1320
APPEARS IN
संबंधित प्रश्न
If nC8 = nC2, find nC2.
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
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?
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?
Compute:
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
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?
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
If 8Cr − 7C3 = 7C2, find r.
If 15Cr : 15Cr − 1 = 11 : 5, find r.
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
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 professor is included.
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
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?
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
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?
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is
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
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.
Find the value of 80C2
Find the value of 15C4 + 15C5
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
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 ______.
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 selections be made?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.
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
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.
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is `(11!)/(5!6!) (9!)(9!)`.
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
Number of selections of at least one letter from the letters of MATHEMATICS, is ______.
