Examples of combinations

by Kurious Fox
  1. Poker Hands: In a game of poker, combinations are used to determine the probability of different hands. For instance, the number of ways to get a full house (three of one kind and two of another kind) is calculated using combinations. In poker, a full house is obtained by selecting 1 rank out of 13 (for the three of a kind), and then 3 cards from the 4 of that rank, and then 1 rank out of the remaining 12, and finally 2 cards from the 4 of that rank. So, the number of ways to get a full house is :
    C = \binom{13}{1} \cdot \binom{4}{3} \cdot \binom{12}{1} \cdot \binom{4}{2} = 3,744
  2. Lottery Drawings: In lottery games, combinations are used to calculate the chances of winning. For example, in a 6/49 lottery game where you must choose 6 numbers out of 49, the number of possible combinations is calculated as “49 choose 6,” i.e.,
    C = \binom{49}{6} = 13,983,816
    So, you see. Chances in win a lottery is way lower than “you’re one in a million”!
  3. Team Selection: If a coach has 12 players and needs to select a starting lineup of 5, they can use combinations to find out how many different lineups can be formed, which is,
    C = \binom{12}{5} = 792
  4. Product Marketing: A retail store that wants to create marketing bundles with 3 items out of 10 possible products would use combinations to determine how many different bundles they could offer. The number of bundles is
    C = \binom{10}{3} = 120
  5. Project Planning: In project management, combinations can be used to calculate the number of ways to assign tasks to team members. For instance, in a team of 5 members, if you want to assign 3 tasks, you can calculate the number of ways as:
    C = \binom{5}{3} = 10
  6. Menu Planning: If you’re planning a menu and want to offer 2 dishes out of 5 possible options, you can use combinations to find out how many different menus you can offer. The number of menus is
    C = \binom{5}{2} = 10

Discover more from Science Comics

Subscribe to get the latest posts sent to your email.

Related Posts

Exponential distribution song

This song helps us better remember the properties of the exponential distribution. The exponential distribution models time between events in a Poisson process, where occurrences are independent at a constant rate. Key features include its probability density and cumulative distribution functions, mean, variance, and memoryless property. It has applications in queueing theory, reliability engineering, and survival analysis.

Leave a Reply

error: Content is protected !!