In how many different ways can a winner and a runnerup of a

In how many different ways can a winner and a runner-up of a contest be chosen from a total of 16 contenders? a) 240 b) 120 C) 256 D) 196 In an office, where 12 men and 7 women ore working, a Christmas decorations\' committee of 5 is to be formed. In how many different ways can it be done, it no more than 3 men can serve on the committee? a) 4.620 b) 7.371 c) 11.628 d) 241 How many different 11-letter words (real or imaginary) can be formed from the letters in the word CHATTANOOGA? a) 39, 916.800 b) 7.920 c) 1.663.200 d) 34.650 A single curd is drawn at random from a dock of 52 cards. Find the probability that the card will be a red picture card or a black 7 or a black 8. a) 5/13 b) 7/8 c) 12/52 d) 5/26

Solution

6) Total number of contenders = 16

out of this one player will be a winner and one will be a runner-up

First any one of the 16 contenders can be a winner. so, a winner can be choosen in 16 ways.

Once a winner is choosen then we are left with 15 contenders and the runner should be choosen among these 15,

so, the runner can be any one of these remaining 15 contenders. that is we have 15 choices to choose a runner-up.

Total number of possibilities to choose a winner and followed by a runner-up =16x15=240

So the correct answer for question number 6 is 240. that is option (a) is correct.

7) We have 12 men and 7 women out of which we have to select 5 members to form a team and we can select atmost three men. This can be done in the following ways

(0 men + 5 women) or (1 man + 4 women) or (2 men + 3 women) or (3 men + 2 women)

0 men and 5 women (that is a team with all 5 women) and be selected in ¹²C₀x⁷C₅=1x21=21

1 man and 4 women can be selected in ¹²C_1x⁷C₄ =12x35=420

2 men and 3 women can be selected in ¹²C_2x⁷C₃ =66x35=2310

3 men and 2 women can be selected in ¹²C_3x⁷C₂ =220x21=4620

The total number of teams = 21+420+2310+4620 = 7371.

So option (b) is correct for question number 7