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Permutations and Combinations

Short Answer Type

191. Find the number of combinations of 5 cards out of 52 cards in a deck if each combination must contain exactly one queen.

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192. From a class of 25 students 4 students are to be selected for a painting competition such that 2 of the students are always included. In how many ways can they be selected?

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193. A box contains 5 different red balls and 6 different white balls. In how many ways can 6 balls be selected, so that there are at least two balls of each colour?

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194. Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

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195.

A bag contains 6 balls each of red, blue, green and yellow colours. In how many ways can 4 balls be drawn from the bag?

(a) In how many of the selections, the balls drawn are of the same colour?

(b) In how many of the selections the balls drawn are all of different colours?

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196. A polygon has 44 diagonals. How many sides does it have?

Solution not provided.

Ans. 11

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197. A polygon has 7 sides. How many diagonals does it have?

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198.

There are 14 points in a plane, 7 of which are collinear. How many

(a) straight lines (b) triangles can be formed by these points?

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199. From amongst 7 Americans, and 5 British diplomats, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to have at least 3 Americans?

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200. From a group of 16 students 8 are to be selected for the songs competition in a school. Two of the students decide that either both of them will be in the group or both of them will not participate. In how many ways can the group of 8 be selected?

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