Advertisements
Advertisements
Question
Five students are selected from 11. How many ways can these students be selected if two specified students are selected?
Advertisements
Solution
5 students are to be selected from 11 students
When 2 specified students are included then remaining 3 students can be selected from (11 – 2) = 9 students.
∴ Number of ways of selecting 3 students from 9 students = 9C3
= `(9!)/(3! xx 6!)`
= `(9 xx 8 xx 7 xx 6!)/(3 xx 2 xx 1 xx 6!)`
= 84
∴ Selection of students is done in 84 ways when 2 specified students are included.
APPEARS IN
RELATED QUESTIONS
Find the value of `""^80"C"_2`
Find the value of `""^15"C"_4 + ""^15"C"_5`
If `""^"n""P"_"r" = 1814400` and `""^"n""C"_"r"` = 45, find r.
Find the number of ways of selecting a team of 3 boys and 2 girls from 6 boys and 4 girls.
After a meeting, every participant shakes hands with every other participants. If the number of handshakes is 66, find the number of participants in the meeting.
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 15
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 12
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear.
Find the number of triangles formed by joining 12 points if no three points are collinear,
Find the number of triangles formed by joining 12 points if four points are collinear.
Find n if `""^"n""C"_8 = ""^"n""C"_12`
Find n, if `""^"n""C"_("n" - 2)` = 15
A group consists of 9 men and 6 women. A team of 6 is to be selected. How many of possible selections will have at least 3 women?
A committee of 10 persons is to be formed from a group of 10 women and 8 men. How many possible committees will have at least 5 women? How many possible committees will have men in the majority?
A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two questions from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
Nine friends decide to go for a picnic in two groups. One group decides to go by car and the other group decides to go by train. Find the number of different ways of doing so if there must be at least 3 friends in each group.
If nPr = 1814400 and nCr = 45, find n+4Cr+3
Find the number of ways of selecting a team of 3 boys and 2 girls from 6 boys and 4 girls
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 15
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 8
Find the number of triangles formed by joining 12 points if four points are collinear
Find n if 21C6n = `""^21"C"_(("n"^2 + 5))`
Find r if 11C4 + 11C5 + 12C6 + 13C7 = 14Cr
Find the differences between the greatest values in the following:
14Cr and 12Cr
Find the differences between the greatest values in the following:
15Cr and 11Cr
Select the correct answer from the given alternatives.
A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 8 from part A and 5 from part B, In how many ways can he choose the questions?
Select the correct answer from the given alternatives.
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently
Answer the following:
A student finds 7 books of his interest but can borrow only three books. He wants to borrow the Chemistry part-II book only if Chemistry Part-I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
Answer the following:
There are 4 doctors and 8 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
In how many ways can a group of 5 boys and 6 girls be formed out of 10 boys and 11 girls?
What is the probability of getting a “FULL HOUSE” in five cards drawn in a poker game from a standard pack of 52-cards?
[A FULL HOUSE consists of 3 cards of the same kind (eg, 3 Kings) and 2 cards of another kind (eg, 2 Aces)]
Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is ______.
