Advertisements
Advertisements
Question
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
Solution
We count the number by INDIRECT method of counting.
Number of ways to select a team of 6 people = 12C6
Number of teams with No doctor in any team = 8C6
Required number = 12C6 – 8C6
= 924 – 28
= 896
APPEARS IN
RELATED QUESTIONS
Find the value of `""^15"C"_4 + ""^15"C"_5`
Find the value of `""^20"C"_16 - ""^19"C"_16`
Find n if `""^"n""C"_("n" - 3)` = 84
If `""^"n""C"_("r" - 1)` = 6435, `""^"n""C"_"r"` = 5005, `""^"n""C"_("r" + 1)` = 3003, find `""^"r""C"_5`.
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 = 10
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 15
A word has 8 consonants and 3 vowels. How many distinct words can be formed if 4 consonants and 12 vowels are chosen?
Find n, if `""^21"C"_(6"n") = ""^21"C"_(("n"^2 + 5)`
Find the differences between the largest values in the following: `""^15"C"_r "and" ""^11"C"_r`
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
Five students are selected from 11. How many ways can these students be selected if two specified students are selected?
Find n if 2nC3 : nC2 = 52 : 3
Find n if nCn–3 = 84
Find n and r if nCr–1 : nCr : nCr+1 = 20 : 35 : 42
If 20 points are marked on a circle, how many chords can be drawn?
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 15
There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection
Find the number of triangles formed by joining 12 points if four points are collinear
Find n if nC8 = nC12
Find n if 23C3n = 23C2n+3
Find n if nCn–2 = 15
Find r if 11C4 + 11C5 + 12C6 + 13C7 = 14Cr
Find the value of `sum_("r" = 1)^4 ""^((21 - "r"))"C"_4`
A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two question from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
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.
A student passes an examination if he secures a minimum in each of the 7 subjects. Find the number of ways a student can fail.
Answer the following:
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7 and 5
Answer the following:
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms formed
The maximum value of z = 9x + 11y subject to 3x + 2y ≤ 12, 2x + 3y ≤ 12, x ≥ 0, y ≥ 0 is _______.
If vertices of a parallelogram are respectively (2, 2), (3, 2), (4, 4), and (3, 4), then the angle between diagonals is ______
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)]
