Advertisements
Advertisements
Question
How many strings can be formed using the letters of the word LOTUS if the word either starts with L or ends with S?
Advertisements
Solution
Either starts with L or ends with S
| L |
The first box is filled with the letter L.
The second box can be filled with the remaining letters O, T, U, S in 4 ways.
The third box can be filled with the remaining letters excluding L and the letter placed in box 2 in 3 ways.
The fourth box can be filled with the remaining letters excluding L and the letters placed in a box – 2 and box – 3 in 2 ways.
The fifth box can be filled with the remaining one letter excluding L and the letters placed in a box – 2 and box – 3, box – 4 in 1 way.
Therefore, by fundamental principle of multiplication
The number of words start with L is = 1 × 4 × 3 × 2 × 1 = 24
| S |
Since the word ends with S, the fifth box can be filled in one way with the letter S.
The remaining four boxes can be filled 4 × 3 × 2 × 1 way.
Therefore, the number of words ending with S = 4 × 3 × 2 × 1 × 1 = 24
Number of words starting with L and ends with S:
The first box can be filled with L in one way
The Fifth box can be filled with S in one way second box,
The Third box and fourth box can be filled in 3 × 2 × 1 ways with the remaining letters O, T, U.
∴ Number of words starting with L and ends with S = 1 × 3 × 2 × 1 × 1 = 6
Therefore, by fundamental principle of addition
Number of words either starts with L or ends with S = 24 + 24 – 6 = 48 – 6 = 42
APPEARS IN
RELATED QUESTIONS
How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?
How many two-letter words can be formed using letters from the word SPACE, when repetition of letters is not allowed?
How many numbers between 100 and 1000 have 4 in the units place?
How many two letter words can be formed using letters from the word SPACE, when repetition of letters is not allowed?
How many numbers formed with the digits 0, 1, 2, 5, 7, 8 will fall between 13 and 1000 if digits can be 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
Three persons enter into a conference hall in which there are 10 seats. In how many ways they can take their seats?
In how many ways 5 persons can be seated in a row?
How many three-digit numbers are there with 3 in the unit place?
with repetition
Count the numbers between 999 and 10000 subject to the condition that there are no digit is repeated
How many three-digit numbers, which are divisible by 5, can be formed using the digits 0, 1, 2, 3, 4, 5 if repetition of digits are not allowed?
Find the value of n if `1/(8!) + 1/(9!) = "n"/(10!)`
Choose the correct alternative:
In an examination there are three multiple choice questions and each question has 5 choices. Number of ways in which a student can fail to get all answer correct i
Choose the correct alternative:
The number of 5 digit numbers all digits of which are odd i
Choose the correct alternative:
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is
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.
The number of possible outcomes when a coin is tossed 6 times is ______.
