Answered

Discover new knowledge and insights with IDNLearn.com's extensive Q&A database. Discover the information you need from our experienced professionals who provide accurate and reliable answers to all your questions.

A catering service offers 12 appetizers, 9 main courses, and 7 desserts. A banquet chairperson is to select 8 appetizers, 8 main courses, and 6 desserts for a banquet. In how many ways can this be done?

Sagot :

Crisforpidn
[(12! / (8!*4!) ]* [9! / (8!*1!) ] * [ 7!/ (6!*1!)] = ( 12 * 11 * 10 * 9 / 4 * 3 * 2 * 1) * 9 * 7 = 45 * 11 * 9 * 7 = 31185 ways
Kate200468idn
[tex]12-appetizers, \ 9- main\ courses, \ 7\ desserts\\ \\ selection:\ 8\ appetizers,\ 8\ main\ courses, 6\ desserts\\\\a=the\ number\ of\ selection\ of\ appetizers:\\ \\{12 \choose 8}= \frac{12!}{8!\cdot (12-8)!} = \frac{12\cdot11\cdot10\cdot9\cdot8!}{8!\cdot4\cdot3\cdot2} =11\cdot5\cdot9=495\\ \\c=the\ number\ of\ selection\ of\ main\ courses:\\ \\{9 \choose 8}= \frac{9!}{8!\cdot (9-8)!} = \frac{9\cdot8!}{8!\cdot 1} =9[/tex]

[tex]d=the\ number\ of\ selection\ of\ desserts:\\ \\{7 \choose 6}= \frac{7!}{6!\cdot (7-6)!} = \frac{7\cdot6!}{6!\cdot 1} =7\\ \\the\ number\ of\ selection\ sets\ the\ banquet:\\ \\a\cdot c\cdot d=495\cdot9\cdot7=31185[/tex]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.