Know Yourself

Problems on Permutations and Combinations: 1. How many words can be formed by using all letters of the word 'TIME' so that the vowels are never together? Solution:                 The word contains 4 different letters. When the vowels always come together, we may treat that whole entity as 1 letter.                 The letters to be arranged are  TM (IE).                  These 3 letters can be arranged in  3 P3 = 3! = 6 ways.                 The vowels in (IE) may be arranged in 2! = 2 ways.                 The number of words each having vowels together = 6*2 =   12.                 The total number of words formed by using all the letters of the given word = 4! = 24.         ...

Problems on Permutations and Combinations: 1. How many words can be formed by using all letters of the word 'POLICE'? Solution:                The word POLICE contain 6 different letters.                 6 P6 = 6! = 6*5*4*3*2*1 = 720. 2. How many words can be formed by using all letters of the word 'TIME' so that the vowels always come together? Solution:                 The word contains 4 different letters. When the vowels always come together, we may treat that whole entity as 1 letter.                 The letters to be arranged are TM (IE).                 These 3 letters can be arranged in  3 P3 = 3! = 6 ways.                 The vowels in (IE) may be arranged in 2! = 2 ways.          ...

Aversion Thesaurus: Noun: dislike             allergy, disfavour, disgust, displeasure, hate, hostility, loathing, repulsion, unwillingness, opposition...                                               Antonyms: like, affection, attachment, love, sympathy. ..                                        Example sentences: ·        Sarah has an  aversion to those plants.   ·       Do they really have an aversion to cats?  

Problems on Permutations and Combinations: 1. 20!/18!               = 20*19* 18! / 18! = 20*19 = 380. 2. 10 P4              n Pr   =  n!/(n-r)!               = 10!/ (6!) = 10*9*8*7*6!/ 6! = 5040. 3.  5 P5               = 5!/0! = 5*4*3*2*1 /1 = 120. 4. 30 C2                 n Cr = n(n-1)(n-2).... to r factors / r!              = 30*29/1*2              = 435.  5.  50 C48                  n Cr =  n Cn-r               = 50 C50-48 =  50 C2 = 50*49/ 1*2 = 1225. 6.  30 C30                  n Pn = 1`        ...

Glimpse Thesaurus: Noun: brief look             glance, peek, sight, slant, quick look...           Verb: look briefly             espy, flash, notice, get an eyeful, spot, view...                                           Antonyms:  stare, look fixedly. ..                                       Example sentences: ·        We got the glimpse of that building while we're riding.  ·        She caught a glimpse of him.  

Answer of Day 109: 7300 Hey friends... We're gonna see problems on Permutations and Combinations from tomorrow. So let's look at those formulae today. Formulae: Factorial Notation n! = n(n-1)(n-2).... 3.2.1. 0! = 1. Permutations: n Pr = n! / (n-r)! All permutations made with the letters a,b,c  by taking two at a time are (ab, ba, ac, ca, bc, cb). All permutations made with the letters a,b,c taking all at a time are (abc, acb, bac, bca, cab, cba). Combinations: n Cr = n(n-1)(n-2).... to r factors / r! n Cr =  n Cn-r  If we want to select 2 out of 3 girls A, B and C. Then the possible selections are AB,BC and CA. All the combinations formed by a,b,c taking two at a time are ab, bc and ca. The only combination that can be formed of 3 letters a,b,c taken all at a time is abc.   ab and ba are two different permutations but they represent the same combination. n Cn =1. n Co = 1.    ...

Ample Thesaurus: Noun: more than necessary             enough, sufficient, abundant, capacious, full, great, lavish, liberal, plenty...                                           Antonyms: insufficient, not enough . ..                                       Example sentences: ·        That amount will be ample for me.  ·        There are ample of dishes to serve.