In a party every person shakes hands with every other person. If there are 105 hands shakes, find the number of person in the party.
A. 15
B. 14
C. 21
D. 25
Answer: Option A
Solution(By Examveda Team)
Let n be the number of persons in the partyNumber of hands shake = 105
Total number of hands shake is given by nC2 Now,
According to the question, $$\eqalign{ & ^n{{\text{C}}_2} = 105 \cr & {\text{or, }}\frac{{n!}}{{2! \times \left( {n - 2} \right)!}} = 105 \cr & {\text{or, }}\frac{{n \times \left( {n - 1} \right)}}{2} = 105 \cr & {\text{or, }}{n^2} - n = 210 \cr & {\text{or, }}{n^2} - n - 210 = 0 \cr & {\text{or, }}n = 15,\, - 14 \cr} $$ But, we cannot take negative value of n So, n = 15
i.e. number of persons in the party = 15
Join The Discussion
Comments ( 3 )
Related Questions on Permutation and Combination
A. 3! 4! 8! 4!
B. 3! 8!
C. 4! 4!
D. 8! 4! 4!
A. 7560,60,1680
B. 7890,120,650
C. 7650,200,4444
D. None of these
A. 8 × 9!
B. 8 × 8!
C. 7 × 9!
D. 9 × 8!
Why 2????? Nc2 ????
@ Ayus, Formula of Combination has been used.
nCr = n!/[r!*(n-r)!]
So,
nC2 = n!/[2!*(n-2)!] as r = 2.
how, n![2!*(n-2)!] =105 came?
plz explain.