हिंदी

Twelve Students Complete in a Race. in How Many Ways First Three Prizes Be Given?

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

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.2 [पृष्ठ १५]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.2 | Q 13 | पृष्ठ १५

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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?


It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?


Compute:

\[\frac{11! - 10!}{9!}\]

Compute:

 L.C.M. (6!, 7!, 8!)


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?


From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?


Since the  number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = `2xx4xx3xx2=48`


How many 3-digit numbers are there, with distinct digits, with each digit odd?


Evaluate the following:

14C3


Evaluate the following:

\[\sum^5_{r = 1} {}^5 C_r\]

 


If nC4 = nC6, find 12Cn.


f 24Cx = 24C2x + 3, find x.


If 8Cr − 7C3 = 7C2, find r.


If n +2C8 : n − 2P4 = 57 : 16, find n.


From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done?


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?


How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?


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.


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 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 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 committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: exactly 3 girls?


A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: at least 3 girls?


A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.


If 15C3r = 15Cr + 3 , then r is equal to


Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?


Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?


If n + 1C3 = 2 · nC2 , then n =


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 20C16 – 19C16 


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?


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.


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 at least one boy and one girl


In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship is ______.


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!)`.


The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` 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 ______.


A regular polygon has 20 sides. The number of triangles that can be drawn by using the vertices but not using the sides is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×