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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.

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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.

Total cards = 52
Number of cards to be selected = 5
Type of cards requried = 1 king + 4 others
We have 4 kings + 48 others.

$rightwards double arrow$ Number of selections = $straight C presuperscript 4 subscript 1 cross times straight C presuperscript 48 subscript 4 space equals space fraction numerator 4 space factorial over denominator 3 factorial space 1 factorial end fraction cross times fraction numerator 48 space factorial over denominator 44 factorial space 4 factorial end fraction$

= $4 cross times fraction numerator 48 cross times 47 cross times 46 cross times 45 over denominator 4 cross times 3 cross times 2 cross times 1 end fraction equals 4 cross times 2 cross times 47 cross times 46 cross times 45$
= 778320

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?

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175.

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

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

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

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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.

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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?

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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