2 votes 2 votes Line up of 7 people: – Mother, Father, 3 sons, 2 daughters • How many line-ups are there in which the mother is next to at least one of her 3 sons? sumit goyal 1 asked Jan 12, 2018 sumit goyal 1 278 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply sumit goyal 1 commented Jan 12, 2018 reply Follow Share provide approach in detail answer not given 0 votes 0 votes Mamta Satywali commented Jan 12, 2018 reply Follow Share Is it 4320? 0 votes 0 votes sumit goyal 1 commented Jan 12, 2018 reply Follow Share Mamta Satywali i took this from a pdf answer not mentioned share your approach so that others can see its correct or not 0 votes 0 votes Mamta Satywali commented Jan 14, 2018 reply Follow Share Mother is next to at least one of her 3 sons=Total possible arrangements - Mother is not next to any one of her 3 sons Mother is next to at least one of her 3 sons=7!- Mother is not next to any one of her 3 sons Let's find cases when the mother is not next to any one of her 3 sons. Case 1: Mom is standing at the extreme positions in line 1. M _ _ _ _ _ _ The 2nd position could be filled by anyone except 3 boys, i.e 2 girls + 1 father =3 Rest 3rd,4th...7th could be filled by remaining 5. hence 5! total=3*5! 2. _ _ _ _ _ _ M Same as above here also 3*5! Total from this case= 2*3*5! Case-2: Mom is not standing in the extreme positions of line X_ _ _ _ _X Selecting any of 5 positions 5C1=5 eg- X_ _ M _ _X Now making sure that to the right & left of 'M' no son appears, select 2 from 3(1 father +2 daughters) i.e 3C2=3 eg- _ _D1 M D2 _ _ Rest 4 could be any hence 4! total=5*3*4! Now, from Case 1 &2, we have 2*3*5! + 5*3*4! =1080 Final ans=7!-1080=5040-1080=3960 #ps- I did some calculation mistake in my previous comment. 0 votes 0 votes Please log in or register to add a comment.
