Advertisements
Advertisements
Question
How many two letter words can be formed using letters from the word SPACE, when repetition of letters is allowed?
Solution
Two-letter word is to be formed out of the letters of the word 'SPACE'.
Number of letters in the word 'SPACE' = n = 5
When repetition of the letters is allowed
First letter can be selected in 5 ways = `""^5"C"_1 = (5!)/(5!(5 - 1)!) = 5`
Second Letter can be selected in 5 ways (as repetition is allowed the letters selected before is also available) = `""^5"C"_1 = (5!)/(5!(5 - 1)!) = 5`
∴ By using the fundamental principle of multiplication,
The total number of 2-lettered words = 5 × 5 = 25.
APPEARS IN
RELATED QUESTIONS
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed?
How many numbers between 100 and 1000 have the digit 7 exactly once?
In a test, 5 questions are of the form 'state, true or false'. No student has got all answers correct. Also, the answer of every student is different. Find the number of students appeared for the test.
If numbers are formed using digits 2, 3, 4, 5, 6 without repetition, how many of them will exceed 400?
How many five-digit numbers formed using the digit 0, 1, 2, 3, 4, 5 are divisible by 5 if digits are not repeated?
Select the correct answer from the given alternatives.
A college offers 5 courses in the morning and 3 in the evening. The number of ways a student can select exactly one course, either in the morning or in the evening
How many words can be formed by writing letters in the word CROWN in different order?
Answer the following:
A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.
Given four flags of different colours, how many different signals can be generated if each signal requires the use of three flags, one below the other?
Four children are running a race:
In how many ways can the first two places be filled?
Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8 if repetitions of digits is allowed
How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5? if the repetition of digits is not allowed
How many strings can be formed using the letters of the word LOTUS if the word neither starts with L nor ends with S?
Find the value of 4! + 5!
Choose the correct alternative:
The number of 10 digit number that can be written by using the digits 2 and 3 is
The number of ways in which a garland can be formed by using 10 identical pink flowers and 9 identical white flowers is ______
In a class, there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class for a function. In how many ways can the teacher make this selection?
Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.
A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing question
Find the number of positive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digit is to be repeated.
