How many words of 4 letters with Orwithout meaning be made from the letters of the word number when repetition of letters is not allowed?

Text Solution

Answer : 7

Solution : There are 10 letters in the word LOGARITHMS. So, the number of 4-letter words is equal to the number of arrangements of 10 letters, taken 4 at a time, i.e., `.^(10)P_(4)=5040`.

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1. How many words of 4 letters with or without meaning be made from the letters of the word ‘NUMBER’, when repetition of letters is not allowed? A) 480 B) 360 C) 240 D) 360 E) 24

   D) 360
   Explanation: NUMBER is 6 letters. We have 4 places where letters are to be placed. For first letter there are 6 choices, since repetition is not allowed, for second, third and fourth letter also we have 5, 4, and 3 choices resp., so total of 6*5*4*3 ways = 360 ways.

   
   
2. In how many ways the letters of the word ‘ALLIGATION’ be arranged taking all the letters? A) 120280 B) 453600 C) 360340 D) 3628800 E) None of these

   B) 453600
   Explanation: ALLIGATION contains 10 letters, so total 10! ways. There are 2 As, 2 Ls, 2 Is So 10!/(2!*2!*2!)

   
   
3. In how many ways all the letters of the word ‘MINIMUM’ be arranged such that all vowels are together? A) 60 B) 30 C) 90 D) 70 E) 120

   A) 60
   Explanation: Take vowels in a box together as one – IIU, M, N, M, M So there are 5 that to be placed for this 5!, now 3 Ms, so 5!/3!, so arrangement of vowels inside box gives 3!/2! So total = 5!/3! * 3!/2!

   
   
4. In how many ways a group of 4 men and 3 women be made out of a total of 8 men and 5 women? A) 720 B) 140 C) 120 D) 360 E) 210

   B) 140
   Explanation:
   Total ways = 8C4*5C3

   
   
5. How many 3 digit numbers are divisible by 4? A) 256 B) 225 C) 198 D) 252 E) 120

   B) 225
   Explanation: A number is divisible by 4 when its last two digits are divisible by 4 For this the numbers should have their last two digits as 00, 04, 08, 12, 16, … 96

   By the formula, an = a + (n-1)d

   96 = 0 + (n-1)*4 n = 25 so there are 25 choices for last 2 digits and 9 choices (1-9) for the 1st digit

   so total 9*25

   
   
6. How many 3 digits numbers have exactly one digit 2 in the number? A) 225 B) 240 C) 120 D) 160 E) 185

   A) 225
   Explanation: 0 cannot be placed at first digit to make it a 3 digit number. 3 cases: Case 1: 2 is placed at first place 1 choice for the first place, 9 choices each for the 2nd and 3rd digit (0-9 except 2) So numbers = 1*9*9 = 81 Case 2: 2 is placed at second place 8 choices for the first place (1-9 except 2), 1 choice for the 2nd digit and 9 choices for the 3rd digit (0-9 except 2) So numbers = 8*1*9 = 72 Case 3: 2 is placed at third place 8 choices for the first place (1-9 except 2), 9 choices for the 2nd digit (0-9 except 2) and 1 choice for the 3rd digit So numbers = 8*9*1 = 72 So total numbers = 81+72+72 = 225

   
   
7. There are 8 men and 7 women. In how many ways a group of 5 people can be made such that the particular woman is always to be included? A) 860 B) 1262 C) 1001 D) 1768 E) 984

   C) 1001
   Explanation: Total 15 people, and a particular woman is to be taken to form a group of 5, so choice is to be done from 14 people of 4 people

   Ways are 14C4.

   
   
8. There are 6 men and 7 women. In how many ways a committee of 4 members can be made such that a particular man is always to be excluded? A) 280 B) 420 C) 220 D) 495 E) 460

   D) 495
   Explanation:
   There are total 13 people, a particular man is to be excluded, so now 12 people are left to chosen from and 4 members to be chosen. So ways are 12C4.
   

   
   
9. How many 4 digit words can be made from the digits 7, 8, 5, 0, and 4 without repetition? A) 70 B) 96 C) 84 D) 48 E) 102

   B) 96
   Explanation: 0 cannot be on first place for it to be a 4 digit number, So for 1st digit 4choices, for second also 4 (because 0 can be placed here), then 3 for third place, 2 for fourth place Total numbers = 4*4*3*2

   
   
10. In how many ways 8 students can be given 3 prizes such that no student receives more than 1 prize? A) 348 B) 284 C) 224 D) 336 E) None of these

    D) 336
    Explanation: For 1st prize there are 8 choices, for 2nd prize, 7 choices, and for 3rd prize – 6 choices left So total ways = 8*7*6

    
    

Answers

Related How many words of 4 letters with or without meaning be made from the letters of the word ‘NUMBER’, when repetition of letters is not allowed?a)480b)24c)240d)360e)None of theseCorrect answer is option 'D'. Can you explain this answer?

NUMBER is 6 letters.

We have 4 places where letters are to be placed.

For first letter there are 6 choices, since repetition is not allowed, for second, third and fourth letter also we have 5, 4, and 3 choices resp., so total of 6*5*4*3 ways = 360 ways.

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