(a) A missile is fired if any of these three conditions are met with respect to

Question

(a) A missile is fired if any of these three conditions are met with respect to a 32-bit register:

(b) C1: exactly 7 bits are set in the upper 16-bits, with all the low-order 16 bits being set;

(c) C2: exactly 3 bits are cleared in the lower 16-bits, with all the higher-order 16 bits being set; or

(d) C3: exactly 7 bits are set in the upper 16-bits, and exactly 3 bits are cleared in the lower 16-bits.

Question:

Why are the Venn diagram spaces for C1, C2, and C3 disjoint? (Answer in 2 sentences.)

Which rule (sum/product) can you use to total-up the number of ways in which the missile can be fired? (Answer in 2 sentences.)

Calculate the total number of distinct ways to fire the missile. (Show all the calculations, including the use of Combinatorics – P(..) or C(..) function, as appropriate.)

Explanation / Answer

a) The venn diagrams for C1,C2 and C3 are disjoint since they are mutually exclusive events occurence of one event will rule out the occurence of the other two events

b) Since the events are mutually exclusive, hence we can find the number of ways that satisfy the C1, C2 and C3 criteria

Total number of ways = C1 criteria is followed + C2 criteria is followed + C3 criteria is followed

c)

C1 = 16C7 * 16C6 = 16C7 ways = 11440 ways

C2 = 16C3 * 16C6 = 16C3 ways = 560 ways

C3 = 16C7 * 16C13 = 560 ways * 11440 ways = 6406400 ways

Total number of ways = 11440 + 560 + 6406400 = 6418400

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