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a) Choose 3 shoes from 10 pairs of shoes such that there is no matching pair of

ID: 3130916 • Letter: A

Question

a) Choose 3 shoes from 10 pairs of shoes such that there is no matching pair of shoes. How many choices are there? (b) Choose 4 digits from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 without replacement to form a four digit number. How many different ways to form an odd number are there? But A four-digit number does not start with 0. a) Choose 3 shoes from 10 pairs of shoes such that there is no matching pair of shoes. How many choices are there? (b) Choose 4 digits from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 without replacement to form a four digit number. How many different ways to form an odd number are there? But A four-digit number does not start with 0.

Explanation / Answer

a. No of choices of picking 3 shoes such that, no matching pair is obtained is ,

TOTAL NUMBER OF CHOICES -

NO OF CHOICES F PICKING SHOES THAT HAS MATCHING PAIR

= 20 c 3 - 2 *10c1*9c1 = 960 choices

b. wehave, 10 digits,

For a four digit odd number, the last digit must be an odd number

Thus, the digit at units place can be filled in 5ways

Now,thefirst digit cannot be zero, thus it can be filled in (9-1) ways

Second digitmay have zero, thus, it can be filled in 8 ways

Third digit can be filed in 7 ways

Totalnumber of different ways to form odd number is = 5*8*8*7= 2240 ways