1) how many diffrent numbers having all 5 digits can be formed using all the digits 3,4,5,6, and 7? without repeatability of digits. how many are divisible by 5?
2) how many 6 letter words can be formed using all the letters of word MONDAY? how many of these begin with M? how many of these end in Y?
3) a shelf contains 8 diffrent books out of which 3 are statics, 3 are of life sci and 2 r of biostats. these 8 are to be arranged such that each appear together . in how many ways, such arrangement can b made?
plz help as much as u can :( with steps if u can ..thanks a lot in advance :)
2) how many 6 letter words can be formed using all the letters of word MONDAY? how many of these begin with M? how many of these end in Y?
3) a shelf contains 8 diffrent books out of which 3 are statics, 3 are of life sci and 2 r of biostats. these 8 are to be arranged such that each appear together . in how many ways, such arrangement can b made?
plz help as much as u can :( with steps if u can ..thanks a lot in advance :)
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1. Total 5 digit numbers = 5! = 5*4*3*2*1 = 120 numbers
Total numbers divisible by = 4*3*2*1*1 = 24 numbers
2. number of words = 6! = 6*5*4*3*2*1 = 720 words (since all letters are distinct)
begin with M =1*5*4*3*2*1 = 120 words
end with Y =*5*4*3*2*1*1 = 120 words
3. 3 kinds of book can be arranged together 3! = 6 ways
3 kinds itself arranged = 3*2*1+3*2*1+2*1 = 6+6+2 = 14ways
Total ways = 6 * 14 = 84
Total numbers divisible by = 4*3*2*1*1 = 24 numbers
2. number of words = 6! = 6*5*4*3*2*1 = 720 words (since all letters are distinct)
begin with M =1*5*4*3*2*1 = 120 words
end with Y =*5*4*3*2*1*1 = 120 words
3. 3 kinds of book can be arranged together 3! = 6 ways
3 kinds itself arranged = 3*2*1+3*2*1+2*1 = 6+6+2 = 14ways
Total ways = 6 * 14 = 84