1. Use a table to list all possible Two-digit numbe rs are formed, from the digi
ID: 3322081 • Letter: 1
Question
1. Use a table to list all possible Two-digit numbe rs are formed, from the digits 7,4,3 a. with replacement b. without replacement 2. A coin is tossed 3 times. D raw a tree-diagram to list the sample space. Use this information to find following 1. II. IlI. List the sample space. Find the outcomes of tossing heads exactly twice Find the outcomes of tossing tails at least twice 3. How many ordered arrangements are there of the letters in the words? I. "STATISTICS" "PHILIPPINES" Suppose you can chose from 3 different shirts, 2 pairs of pants, and 5 pairs of shoes, find out how many different outfit you can make? Il.Explanation / Answer
3) When a word containig n letters are where a letters of 1 type b of another type and so on are repeated, then total number of ordered arrangements = n!/(a! * b!*c!....)
(a) S T A T I S T I C S has a total of 10 letters where S comes thrice, T come thrice and I comes twice.
Therefore number of ordered arrangements = 10!/(3!*3!*2!) = 50,400 arrangements.
PHILIPPINES has a total of 11 letters where P comes thrice and I comes thrice.
Therefore number of ordered arrangements = 11!/(3!*3!) = 1,108,800 arrangements
(b) You can chose 1 shirt from 3 shirts in 3 ways. (Either S1, S2 or S3)
You can choose 1 pair of pants from 2 pants in 2 ways. (P1 or P2)
You can choose 1 pair of shoes from 5 pairs in 5 ways. (SH1, SH2, SH3, SH4 or SH5)
Therefore total number of combinations = 3 * 2 * 5 = 30 outfits.
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