Please answer the above questions regarding combinations in DETAIL. Thank you :)

Question

Please answer the above questions regarding combinations in DETAIL. Thank you :)

c) [1+2+2 5 marks] In a tutorial class for COS10003 on binary numbers, six students have been given a large sheet of paper with a 1 on it and six students have been given a large sheet of paper with a 0 on it. If four students are needed for a demonstration of 4-bit numbers, answer the following questions with your working. i. How many different groups of four students can be formed? How many different combinations contain two 1's and two O's? ii. How many different combinations contain at least two 1's?

Explanation / Answer

Question (c)

Here there six '1' binary numbers and six '0' binary numbers.

(i) So number of different groups of four students possible = 4C0 * 4C4 + 4C1 * 4C3 + 4C24C2 + 4C3 * 4C1 + 4C0 * 4C4 = 1 + 4 * 4 + 6 * 6 + 4 * 4 + 1 * 1 = 70

(ii) Here total number of different combinations of two 1's and two 0 's .

Total combinations are

space = (1100), (1010), (1001), (0110), (0011) , (0101) = total 6 such combinations

(iii) At least two 1's.

Exactly two 1's = (1100), (1010), (1001), (0110), (0011) , (0101)

Exactly three 1's = (1110), (1101), (1011), (0111)

Exactly four 1's = (1111)

So total 11 such combinmations arer there,

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