Use the information given below to answer the next question.For a soccer match between Germany and Argentina, 7 Germans and 5 Argentines are standing at the ticket counter to buy the tickets. Every ticket bears a seat number and the people with tickets bearing consecutive seat numbers sit together. The person issuing tickets at the counter is advised not to issue tickets bearing consecutive seat numbers to two Argentines.In how many ways can the tickets be issued?AnswerPlease choose a correct answer. CLEARUNSOLVED7! × 5! × 8C57! × 8C55! × 8C57! × 5!
Question
Use the information given below to answer the next question.For a soccer match between Germany and Argentina, 7 Germans and 5 Argentines are standing at the ticket counter to buy the tickets. Every ticket bears a seat number and the people with tickets bearing consecutive seat numbers sit together. The person issuing tickets at the counter is advised not to issue tickets bearing consecutive seat numbers to two Argentines.In how many ways can the tickets be issued?AnswerPlease choose a correct answer. CLEARUNSOLVED7! × 5! × 8C57! × 8C55! × 8C57! × 5!
Solution
Firstly, the 7 Germans can be arranged in 7! ways.
Now, consider the Germans and the spaces between them. There are 8 such spaces (before the first German, between the Germans, and after the last German).
The 5 Argentines must be placed in these spaces such that no two Argentines are in consecutive spaces. This can be done in 8C5 ways.
So, the total number of ways the tickets can be issued is 7! * 8C5.
Therefore, the correct answer is 7! * 8C5.
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