$$\left( {{}^{75}{P_2} - {}^{75}{C_2}} \right) = ?$$
A. 0
B. 75
C. 150
D. 2775
E. 5550
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & = \left( {{}^{75}{P_2} - {}^{75}{C_2}} \right) \cr & = \left\{ {\frac{{75!}}{{75! - 2!}} - \frac{{75 \times 74}}{2}} \right\} \cr & = \frac{{75!}}{{73!}} - \left( {75 \times 37} \right) \cr & = \frac{{75 \times 74 \times 73!}}{{73!}} - \left( {75 \times 37} \right) \cr & = \left( {75 \times 74 - 75 \times 37} \right) \cr & = 75 \times 37 \times \left( {2 - 1} \right) \cr & = \left( {75 \times 37} \right) \cr & = 2775 \cr} $$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!
Join The Discussion