Question

i. How many 5-letter passwords (letters may be repeated) can be created from the monkey type- writer from Q1 if it is forbidden for a password to begin and end with the same letter? Answer: 11. Using the monkey typewriter from Q1, how many 8-letter words are there consisting of 8 distinct letters that contain the word 'APE' (as 3 consecutive) letters within the 8-letter word? Answer: iii. Suppose that a group of 9 inhabitants of the Island of Knights & Knaves need to create a committee of 6 members so that the number of knights on the committee is greater than or equal to the number of knaves. In how many ways is it possible to create such a committee given the following information: of these 9 inhabitants, 5 are knights, namely A, B, C, D, and E, and of these 9 inhabitants, the other 4 are knaves, namely W, X, Y and Z. Answer: iv. What is the coefficient of a 163 in the expansion of (2a3 Answer:

Answer 1

Griveu tuot estri Ctio u ist (iy Co tuee ve 121.lo. 1.3 wa

6. 12.11 10.9-8 70 2lt

74. tv) αγ