Advertisements
Advertisements
Question
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
Advertisements
Solution
Two particular books are selected from 10 books. So, 2 books need to be selected from 8 books.
Required number of ways if 2 particular books are always selected =\[{}^8 C_2 = \frac{8}{2} \times \frac{7}{1} = 28\]
APPEARS IN
RELATED QUESTIONS
If nC8 = nC2, find nC2.
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
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:
(i) exactly 3 girls?
(ii) atleast 3 girls?
(iii) atmost 3 girls?
In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?
A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?
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?
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?
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`
In how many ways can six persons be seated in a row?
Evaluate the following:
35C35
If nC4 , nC5 and nC6 are in A.P., then find n.
If 16Cr = 16Cr + 2, find rC4.
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
Find the number of (ii) triangles
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 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?
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?
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 20Cr = 20Cr + 4 , then rC3 is equal to
If nC12 = nC8 , then n =
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?
There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?
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 the value of 15C4 + 15C5
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
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 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 can be of any colour
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?
If nC12 = nC8, then n is equal to ______.
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 ______.
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.
