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Answered

B. Compute for the number of permutations
1. How many distinct permutations can be formed from the letters of the word
MATHEMATICS?

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2. How many ways can 6 different keys be arranged in a key ring?
3. How many three-letter words can be formed from the letters in the word
VIRUS?
4. In how many ways can 8 chairs be arranged in a row?
5. In how many ways can 3 officers consisting of president, secretary, and
treasurer be chosen from a group of 11 members?​

Sagot :

Answer:

1. MATHEMATICS = 11 letters

P(n,r) = P(11,11)  

= 11!/(11−11)!

= 3.99168E+7

= 39,916,800

Repeated letters: 2 M, 2 A, 2 T

39,916,800/(2!2!2!) = 4,989,600 ways

2. P(n,r) = P(6,6)  

= 6!/(6−6)!

= 720 ways

3. VIRUS = 5 letters

P(n,r) = P(5,3)

= 5!/(5−3)!

= 60 ways

4. P(n,r) = P(8,8)  

= 8!/(8−8)!

= 40,320 ways

5. P(n,r) = P(11,3)  

= 11!/(11−3)!

= 990 ways

C41992IN

Answer:

1. 4,989,600

2. 720

3. 20

4. 42320

5. 165

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