Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • In a race, there are 8 male participants and 4 female participants. In how many ways can the gold, silver, and bronze medals be awarded if at least one medal must be won

In a race, there are 8 male participants and 4 female participants. In how many ways can the gold, silver, and bronze medals be awarded if at least one medal must be won by a female participant?

 

Option: 1

1,008 ways


Option: 2

172,864 ways.


Option: 3

4,032 ways


Option: 4

8,064 ways


Answers (1)

To solve this, we will consider the different possible cases based on the number of medals won by female participants:

Case 1: One medal won by a female participant:

Choose 1 female participant for the gold medal (4 choices).

Choose 1 male participant for the silver medal (8 choices).

Choose 1 male participant for the bronze medal (7 choices).

The remaining 6 male participants can be assigned in 6! ways (6 factorial).

Case 2: Two medals won by female participants:

Choose 2 female participants for the gold and silver medals (4 choices for the gold, 3 choices for the silver).

Choose 1 male participant for the bronze medal (8 choices).

The remaining 5 male participants can be assigned in 5! ways.

Case 3: Three medals won by female participants:

Choose 3 female participants for the gold, silver, and bronze medals (4 choices for each medal).

To find the total number of ways, we sum the possibilities for each case:

Case 1: 4 choices × 8 choices × 7 choices × 6! = 4 × 8 × 7 × 720 = 161,280 ways

Case 2: 4 choices × 3 choices × 8 choices × 5! = 4 × 3 × 8 × 120 = 11,520 ways

Case 3: 4 choices × 4 choices × 4 choices = 64 ways

Total: 161,280 + 11,520 + 64 = 172,864 ways.

 

Posted by

Kshitij

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026 application correction begins on jeemain.nta.nic.in; edit details by December 2
anam-khan

JEE Mains 2026 LIVE: NTA to conduct session 1 from January 21 to 30; exam pattern, syllabus
anam-khan

JEE Main 2026 correction window opens tomorrow; NTA allows exam city change

Latest Question