HOW MANY STRINGS CAN BE FORMED WITH THE GIVEN WORD

Question 1 :

How many strings can be formed using the letters of the word LOTUS if the word (i) either starts with L or ends with S? (ii) neither starts with L nor ends with S?

Solution :

Question 3 :

(i) Count the total number of ways of answering 6 objective type questions, each question having 4 choices.

(ii) In how many ways 10 pigeons can be placed in 3 different pigeon holes ?

(iii) Find the number of ways of distributing 12 distinct prizes to 10 students?

Solution :

(i)  Each question is having 4 options.There are 4 ways to answer each question.

1^st question  =  4 ways

2^nd question  =  4 ways  .........

Total number of ways  =  4⁶

(ii) In how many ways 10 pigeons can be placed in 3 different pigeon holes ?

Note : If n different objects are to be placed in m places, then the number of ways of placing is mⁿ.

10  -  Number of pigeons (different things)

3  -  Number of places (pigeon holes)

Applying the formula mⁿ,

Total number of ways  =  3¹⁰

(iii)  12  -  Number of prizes (different things)

10  -  Number of place (students)

Applying the formula mⁿ,

Total number of ways  =  10¹²

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