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Permutations and Combinations

Long Answer Type

171. 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 (ii) at least one boy and one girl (iii) at least 3 girls.

200 Views

Short Answer Type

172.

Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

90 Views

Long Answer Type

173.

What is the number of ways of choosing 4 cards from a pack of 52 cards? In how many of these :

(i) four cards are of the same suit?

(ii) four cards belongs to different suit?

(iii) are face cards?

(iv) two are red cards and two are black cards?

(v) cards are of the same colour?

137 Views

Short Answer Type

174.

How many chords can be drawn through 21 points on a circle?

142 Views

175.
How many straight lines can be formed with 7 points, 3 of which are colinear.

Total number of points = 7.
Number of straight lines formed by these 7 points (no three of which are collinear) by taking 2 at a time

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It is a given that three points are collinear. If these three points are considered to be distinct, number of straight lines formed by these 3 points by taking 2 at a time = $straight C presuperscript 3 subscript 2 space equals space 3 over 1 equals 3.$
Instead of these three lines, the 3 collinear points will give us only 1 line.
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Hence, the number of straight lines formed with 7 points, 3 of which are collinear = 19

103 Views

176. Find the number of triangles formed by 9 points lying on the circumference of a circle.

114 Views

177. Find the number of triangles formed by 12 points, 5 of which are collinear.

92 Views

178.

If $straight C presuperscript straight n minus 1 end presuperscript subscript straight r colon straight C presuperscript straight n subscript straight r colon straight C presuperscript straight n plus 1 end presuperscript subscript straight r space equals space 6 colon 9 colon 13 comma$ Find n and r.

89 Views

179. In an examination, a question paper consists of 12 questions, divided into two parts i.e., Part I and Part II containing 5 and 7 questions respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can the student select his questions?

111 Views

180. From a class of 25 students, 10 are to be chosen for an excursion party. There are three students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

99 Views