Answer:
Step-by-step explanation:
3 or less than 3 tires among the 10 tires should be blemished.
There are some possibilities.
1000 tires are blemished, (5000 - 1000) = 4000 tires are not blemished.
From the 5000 tires, 10 tires can be chosen in [tex]^{5000}C_{10}[/tex] ways.
Possibility 1: 3 tires are blemished.
Total 10 tires can be chosen with 3 blemished tires in [tex]^{1000}C_3 \times {4000}C_7[/tex] ways.
Possibility 2: 2 tires are blemished.
Total 10 tires can be chosen with 2 blemished tires in [tex]^{1000}C_2 \times ^{4000}C_8[/tex] ways.
Possibility 3: 1 tires are blemished.
Total 10 tires can be chosen with 1 blemished tires in [tex]^{1000}C_1 \times^{4000}C_9[/tex] ways.
Possibility 4: No tires are blemished.
Total 10 tires can be chosen with no blemished tires in [tex]^{1000}C_0 \times^{4000}C_{10}[/tex] ways.
Hence, the required probability is [tex]\frac{^{1000}C_1 \times^{4000}C_9 + ^{1000}C_0 \times^{4000}C_{10} + ^{1000}C_2 \times^{4000}C_8 + ^{1000}C_3 \times^{4000}C_7}{^{5000}C_{10} }[/tex].
