Let A be the set of 26 letters of the alphabet, in lowercase. Let S be the set o

Question

Let A be the set of 26 letters of the alphabet, in lowercase. Let S be the set of six-long letter strings, in which letters may repeat. Find the size of each of the following subsets. (Your answer can be a number, or a product. You may use nCk for “n choose k”.)

IC 2.3-20 Counting Practice Exercise 1. What are the values of the combinations: 25 25 25 25 25 23 Exercise 2. Let A be the set of 26 letters of the alphabet, in lowercase. Let S be the set of six-long letter strings, in which letters may repeat. Find the size of each of the following subsets. (Your answer can be a number, or a product. You may use nCk for "n choose k".) (A) S itself. (B) The subset B CS of all strings in which no letter appears more than once (C) The subset C in which the letters a, e, i, o, u do not appear (D) The subset D in which the fourth and last letters agree. (The same letter may appear elsewhere.) (E) The subset E in which only the fourth and last letters agree. That is, no other letters in two different positions agree. (F) The subset F all strings that contain exactly three copies of the letter

Explanation / Answer

Question 1

Formula for combination is nCr=n!/(r!*(n-r)!)

A) 25C0 = 25!/(0!*25!)=1

B) 25C25=25!/(25!*0!)=1

C) 25C3=25!/(3!*22!)=(25*24*23)/(3*2*1)=2300

D) 25C23=25!/(23!*2!)=(25*24)/(2*1)=300

Per Cheg guidelines I have answered first out of the two questions asked. Thankyou

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