PERMUTATION AND COMBINATION - 3

NUMERICAL

Four visitors A,B,C & D arrive at a town which has 5 hotels. In how many ways can they disperse themselves among 5 hotels, if 4 hotels are used to accommodate them.

Ans. A has 5 possibility
B has 4 possibility
C has 3 possibility
D has 2 possibility

Now we have the possibility but everything has to be done simultaneously so,
Multiplication rule will be used.

TOTAL POSSIBILITY ARE = 5*4*3*2 = 120

In how many ways can 5 letters be mailed if there are 3 mailboxes available if each letter can be mail in any mailbox.

   Ans. letter 1  has 3 possibility

letter 2 has 3 possibility
letter 3 has 3 possibility
letter 4 has 3 possibility
letter 5 has 3 possibility

    Everything has to be done simultaneously 
    So, 3*3*3*3*3 = 243

Every telephone number consists of 7 digits. How many telephone numbers are there which do not include any other digits but 2,3,5 & 7 ?

   Ans.  Digit 1 has 4 possibility

Digit 2 has 4 possibility
Digit 3 has 4 possibility
Digit 4 has 4 possibility
Digit 5 has 4 possibility
Digit 6 has 4 possibility
Digit 7 has 4 possibility

    Everything has to be done simultaneously 
    So, 4^7.

Find the number of 5 lettered palindromes which can be formed using the letter from the english alphabet ?

   Ans.  The total alphabet is 26. 

Letter 1 has 26 possibility
Letter 2 has 26 possibility
Letter 3 has 26 possibility
Letter 4 has 1 possibility
Letter 5 has 1 possibility

    Everything has to be done simultaneously 

    So, 26*26*26*1*1 = 26^3.

How many 10 digit numbers can be made with an odd digit so that no two consecutive digits are the same ?

   Ans.  The consecutive digits must not be the same.

    Odd number 1,3,5,7,9.

Digit 1 has 5 possibility
Digit 2 has 4 possibility
Digit 3 has 4 possibility
Digit 4 has 4 possibility
Digit 5 has 4 possibility
Digit 6 has 4 possibility
Digit 7 has 4 possibility
Digit 8 has 4 possibility
Digit 9 has 4 possibility
Digit 10 has 4 possibility

    Everything has to be done simultaneously 

    So, 5* 4^9.

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