Advertisements
Advertisements
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?
Advertisements
उत्तर
2 courses are compulsory out of the 9 available courses. There are 7 more courses.
So, we need to choose 3 courses out of 7 courses.
∴ Required number of ways =\[{}^7 C_3 = \frac{7}{3} \times \frac{6}{2} \times \frac{5}{1} = 35\]
APPEARS IN
संबंधित प्रश्न
If nC8 = nC2, find nC2.
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.
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 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?
How many three-digit odd numbers are there?
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`
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.
Evaluate the following:
14C3
If 15Cr : 15Cr − 1 = 11 : 5, find r.
A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions?
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 group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (ii) at least one boy and one girl?
Find the number of (ii) triangles
Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
If C (n, 12) = C (n, 8), then C (22, n) is equal to
If nC12 = nC8 , then n =
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
If n + 1C3 = 2 · nC2 , then n =
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
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.
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
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
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.
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?
In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 2 particular players?
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to ______.
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 ______.
There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.
There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is ______.
There are 12 persons seated in a line. Number of ways in which 3 persons can be selected such that atleast two of them are consecutive, 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 ______.
