Each Sunday I go to a bakery shop to buy a dozen (12) bread. Beginning on...

Each Sunday I go to a bakery shop to buy a dozen (12) bread. Beginning on that Sunday and continuing through the following Saturday (7 days) I consume either 1 or 2 of the bread each day. Today, Sunday, I find that the bakery mistakenly gave me only 11 bread. In how many ways may I consume all of the bread I got this week? (For example, I might eat 2 today, 1 tomorrow, etc.)

Expert Solution

The situation is to consume 11 breads in 7 days, and each day, either 1 or 2 breads are consumed. We need to find the number of ways this can happen. So, in mathematical terms, we need to find the number of ways of writing 11 as a sum of 7 numbers, all of which are either 1 or 2.

That is possible only if we have 3 1's and 4 2's. You can check that no othet option is there to break 11 as a sum of 7 such numbers. So now, the only problem remains to find ways of assigning 1's and 2's to these 7 days, and mind that the order of assigning matters. This is an example of permutations with repititions, so we use the formula that number of reqd ways is n! ÷ (n1 ! * n2 !) Where n=7, total numbers to be permuted, n1=3, repitition of 1's , n2=4, repitition of 2's.

Therefore answer is 7! ÷( 3!*4!) Which also equals 7C3, that is choosing 3 days out of 7 days and assigning value 1, remaining days assign the value 2.

Hence answer is 35.

Please ask any doubts regarding this ib the comments below, and give a thumbs up if the solution helps. Happy to help!

orchestra answered 1 year ago

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