In a question paper, there are four multiple-choice questions. Each question has five choices with only one choice for its correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?
Correct Answer is: 624
Each of 2 women and 3 men is to occupy one chair out of 8 chairs, each of which is numbered from 1 to 8. First, women are to occupy any two chairs from those numbered 1 to 4; and then the 3 men would occupy any three chairs out of the remaining 6 chairs. What is the maximum number of different ways in which this can be done?
Correct Answer is: 1440
Since 2 females can sit on the chairs numbered 1 to 4 in 4P2 = 12 ways.
And on remaining 6 chairs, 3 males can sit in 6P3=120 ways
Total no of required arrangements: 12X120=1440
How many numbers are there in all from 6000 to 6999 (Both 6000 and 6999 included) having at least one of their digits repeated?
Correct Answer is: 496
All the six letters of the name SACHIN are arranged to form different words without repeating any letter in anyone word. The words so formed are then arranged as in a dictionary.
What will be the position of the word SACHIN in that sequence?
Correct Answer is: 601
Nine different letters are to be dropped in three different letter boxes. In how many different ways can this be done?
Correct Answer is: 3^9
Three dice (each having six faces with each face having one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one dice shows the number 2?
Correct Answer is: 91
The No of total such results in which digit 2 is shown at least one dice = (total results) - (results which don't show the digit 2 )
= 6^3-5^3 = 216-125=91
Groups each containing 3 boys are to be formed out of 5 boys — A, B, C, D and E such that no one group contains both C and D together. What is the maximum number of such different groups?
Correct Answer is: 7
ABC, ABD, ABE, BCE, BDE, CEA, DEA
Three flags, each of different colour, are available for a military exercise. Using these flags, different codes can be generated by waving
(i)single flag of different colours, or
(ii)any two flags in a different sequence of colours, or
(iii)three flags in a different sequence of colours.
The maximum number of codes that can be generated is...........
Correct Answer is: 15
Each of the 3 persons is to be given identical items such that product of the numbers of items received by each of the three persons is equal to 30. In how many maximum different ways can this distribution be done?
Correct Answer is: 27
A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blind-folded (without replacing any of it) to be assured of picking atleast one ball of each colour?