These 8 doctors are chosen chosen from a group of 17 among which there are 6 surgeons. Hence, 210 different committees are three if only the primary school is represented.Ī hospital decides to send a delegation of 8 doctors to a conference. We have to select 6 people of these 10 delegates to form a committee. Number of delegates from primary school = 10. Hence, 38760 different committees are three. We have to select 6 people of these 20 delegates to form a committee. How many different committees are there?ī. How many different committees are there if only the primary school is represented? A committee of 6 people is to be formed.Ī. Hence, the rank or order of the word ZENITH is 616.Ī committee of parents is made up of 20 delegates of which 10 represent the primary school, 6 the intermediate school and 4 the secondary school. Number of words can be formed starting with E,H and so on. Number of new words formed with the letters of the word.Īlphabetical order of the letters of the word ZENITH isĭictionary gives meanings in the order starting with E,H and so on. If all the words are written in a dictionary, what is the rank or order of the word ZENITH ? The letters of the word ZENITH are written in all possible orders. If all four are different, 4 from 8 different letters If 2 are alike and other 2 are different, any one of the three groupsĪnd 2 letters from 7 different letters are selected. If 2 are alike and other 2 are also alike, any 2 of the 3 groups The group of 4 letters can be selected in any one of the following 4 forms. Thus, we have 11 letters of 8 different kinds as given below. There are 11 letters in the word of which A,I,N are repeated twice. The number of ways in which the room can be lighted isįind the number of ways of selecting 4 letters from the word EXAMINATION. So, in these 3 ways, room can not be lighted) (It includes selecting only two defective bulbs. Number of ways of selecting 2 defective bulbs out of 3 is So, in these 10 ways, room may be lighted or may not be lighted) (It includes selecting two good bulbs, two defective bulbs, one good bulb and one defective bulb. Since there are two bulb points, we have to select 2 out of 5 bulbs. One bulb (or two bulbs) in good condition is enough to light the room. Given : 3 bulbs are defective out of 5.There are two bulb points in the dark room. Find the number of trials in which the room can be lighted. The possible combinations in which it can give a majority decision reversing the lower court areįive bulbs of which three are defective are to be tried in two bulb points in a dark room. In total of 9 cases (6 + 3 = 9), it may give 5 or 6 or 7 or 8 or 9 decisions reversing the lower court. Reversing a lower court means, opposing it for its decision. Upholding a lower court means, supporting it for its decision. Find the number of ways it can give a majority decision reversing the lower court. The supreme court has given a 6 to 3 decisions upholding a lower court. In how many ways can this be done if in the committee there must be at least one member from each group and at least 3 artists ?įor the given condition, possible ways to select members for a committee of 7 members. A committee of 7 members is to be chosen from 6 artists, 4 singers and 5 writers.
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