COURSE OVERVIEW Basic and Advance concept for QUANTITATIVE SECTION 0 GMAT, GRE, SAT Beneficial for those taking any of the tests mentioned above Or those who want to improve their basic concepts
ABOUT ME Amit Kumar Jha B. Tech Won All India Merit Scholorship Teaching Quant for GMAT, GRE, SAT 17 years) Like comment and share https://unacademy.com/user/AmitJha-9460
There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period? 5 subjects can be arranged in 6 periods in 'Ps ways. Any of the 5 subjects can be organized in the remaining period (5C1 ways). Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting. Total number of arrangements 6P5x 5C121=1800
In how many ways can 5 man draw water from 5 taps if no tap can be used more than once? 1st man can draw water from any of the 5 taps. 2nd man can draw water from any of the remaining 4 taps. 3rd man can draw water from any of the remaining 3 taps. 4th man can draw water from any of the remaining 2 taps. 5th man can draw water from remaining 1 tap. 54 3 2 1 Hence total number of ways 5 4x3x2x1=120
Find out the number of ways in which 6 rings of different types can be worn in 3 fingers? The first ring can be worn in any of the 3 fingers (3 ways). Similarly each of the remaining 5 rings also can be worn in 3 ways. Hence total number of ways 3x3x3 3x3x3=36=729
How many different words can we make using the letters A, B, E and L? Solution: We have 4 choices for the first letter, 3 choices for the second letter, 2 choices for the third letter and 1 choice for the fourth letter. Hence the number of words is given by 4*3*2*1=41 = 24
e In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants. Let us mark these positions as under: Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5 Number of ways of arranging the vowels Ps 3! 6. Also, the 3 consonants can be arranged at the remaining 3 positions Number of ways of these arrangements = 3P3-31 = 6 Total number of ways = (6 x 6) = 36.
How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS, if repetition of letters is not allowed? LOGARITHMS contains 10 different letters. Required number of words = Number of arrangements of 10 letters, taking 4 at a time. -10P4 - (10 x 9 x 8 x 7) = 5040.
Amit Kumar Jha
I am K-12 online math teacher. I have also been teaching Quant for GMAT,GRE, SAT n ACT for last 17 years with good results and feedback .