3) (2 pts) How many distinguishable arrangements can be made from a word COLLABO

Question

3) (2 pts) How many distinguishable arrangements can be made from a word COLLABORATION? 4) (2 pts) Given C3 7P3 What connection would you put in between: ? Explain. 5) (2 pt) How many radio station names with three-letter can be formed if the first letter must be W or K; on the second position no W and K are allowed; on the third places all letters can be used. 6) (2 pts) From a group of 6 people, in how many ways can a president and a treasurer be selected? THINK WHAT TO USE: PERMUTATIONS? COMBINATIONS?

Explanation / Answer

Solution:

( 3 )

Given word

  COLLABORATION

here repeated alfabets are

O = 3 times

L = 2 times

A = 2 times

total distinguishable arrngements = (13!) / ( 3!*2!*2!) = 259459200

( 4 )

Given, 7C3 , 7P3

if  7C3 /  7P3 = ( 7!/(3!(7-3)!) / 7!/(7-3)!) = 1 / 3!

3!  7C3 = 7P3  

( 5 )

number of names with first letter either W or K and second letter neither W nor k and third letter may be any alfabet

= 2 * 24 * 26

= 1248

( 6 )

number of ways of selecting a president and a treasurer from group of 6 people = 6P2 = 30

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