Find the value of ${^{75}P_2}-{^{75}C_2}$
Answer & explanation
Correct answer: option 3
${^{75}P_2}-{^{75}C_2}$
= \(\frac{ 75 !}{ 75!- 2! }\) - \(\frac{ 75 !}{ (75!- 2!) . 2! }\)
= \(\frac{ 75 ×74 ×73 !}{ 73! }\) - \(\frac{ 75 !}{ (73!) × 2! }\)
= 75 ×74 - \(\frac{ 75 ×74 }{ 2 ×1 }\)
= 5550 - 2775
= 2775
The correct answer is option (3) : 2775