Answer: 1) 5040 and 2) 165
Step-by-step explanation:
1) Here total number of letters = 10
The number of permutations that can be formed using 4 letters at a time
= P (10, 4)
= [tex]10_P_4[/tex]
= [tex]\frac{10!}{(10-4)!}[/tex]
= [tex]\frac{10!}{6!}[/tex]
= [tex]\frac{10\times 9\times 8\times 7\times 6!}{6!}[/tex]
= 10 × 9 × 8 × 7
= 5040
2) Here the total number of machine = 11
The different combinations of machines can Geoff choose from to use
= [tex]11_C_3[/tex]
= [tex]\frac{11!}{(11-3)!3!}[/tex]
= [tex]\frac{11!}{8!3!}[/tex]
= [tex]\frac{11\times 10\times 9\times 8!}{8!\times 6}[/tex]
= 11 × 5 × 3
= 165
