###### Advertisements

###### Advertisements

From 20 raffle tickets in a hat, four tickets are to be selected in order. The holder of the first ticket wins a car, the second a motor cycle, the third a bicycle and the fourth a skateboard. In how many different ways can these prizes be awarded?

###### Advertisements

#### Solution

The first price can be awarded in 20 different ways.

- The second prize can be awarded in 19 ways.
- The third prize can be awarded in 18 ways.
- The fourth prize can be awarded in 17 ways.

∴ By fundamental principle of multiplication, the total nimber of ways the prizes can be awarded is = 20 + 19 + 18 + 17 = 74

#### APPEARS IN

#### RELATED QUESTIONS

If ^{n}P_{r} = 1680 and ^{n}C_{r} = 70, find n and r.

If four dice are rolled, find the number of possible outcomes in which atleast one die shows 2.

If a polygon has 44 diagonals, find the number of its sides.

A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this can be done when

- atleast two ladies are included.
- atmost two ladies are included.

Let there be 3 red, 2 yellow and 2 green signal flags. How many different signals are possible if we wish to make signals by arranging all of them vertically on a staff?

If nC_{3} = nC_{2} then the value of nC_{4} is:

The value of n, when np_{2} = 20 is:

The number of ways selecting 4 players out of 5 is

The number of diagonals in a polygon of n sides is equal to

The number of 3 letter words that can be formed from the letters of the word ‘NUMBER’ when the repetition is allowed are:

If `""^15"C"_(2"r" - 1) = ""^15"C"_(2"r" + 4)`, find r

If ^{n}P_{r} = 720 and ^{n}C_{r} = 120, find n, r

Prove that ^{15}C_{3} + 2 × ^{15}C_{4} + ^{15}C_{5} = ^{17}C_{5}

Prove that `""^35"C"_5 + sum_("r" = 0)^4 ""^((39 - "r"))"C"_4` = ^{40}C_{5}

If `""^(("n" + 1))"C"_8 : ""^(("n" - 3))"P"_4` = 57 : 16, find the value of n

How many chords can be drawn through 20 points on a circle?

Find the total number of subsets of a set with

[Hint: ^{n}C_{0} + ^{n}C_{1} + ^{n}C_{2} + ... + ^{n}C_{n} = 2^{n}] 4 elements

A trust has 25 members. In how many ways can a President, Vice President and a Secretary be selected?

How many different selections of 5 books can be made from 12 different books if, Two particular books are always selected?

There are 5 teachers and 20 students. Out of them a committee of 2 teachers and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees a particular teacher is included?

There are 5 teachers and 20 students. Out of them a committee of 2 teachers and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees a particular student is excluded?

7 relatives of a man comprises 4 ladies and 3 gentlemen, his wife also has 7 relatives; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man’s relative and 3 of the wife’ s relatives?

A polygon has 90 diagonals. Find the number of its sides?

Choose the correct alternative:

The number of ways in which a host lady invite 8 people for a party of 8 out of 12 people of whom two do not want to attend the party together is

Choose the correct alternative:

The number of ways of choosing 5 cards out of a deck of 52 cards which include at least one king is

Choose the correct alternative:

The number of rectangles that a chessboard has ______

Choose the correct alternative:

If ^{n}C_{4}, ^{n}C_{5}, ^{n}C_{6} are in AP the value of n can be