Randomly select a 7 digit natural number. a) Find the probability that the number has 4...

Randomly select a 7 digit natural number.
a) Find the probability that the number has 4 odd digits, 3 even numbers, and no number is repeated.
b) Find the probability that the number 2 is present exactly 2 times, the number 3 is present exactly 3 times, the remaining digits are present no more than 1 time.

Solutions

Expert Solution

a) We have there are 5 even numbers (0,2,4,6,8) and 5 odd numbers (1,3,5,7,9). Note that 0 is even. The number has 4 odd digits, 3 even numbers, and no number is repeated. The number of possible numbers with this feature is

From this number we have to subtract those numbers starting with 0. The number of 7 digit numbers starting with 0 is

The possible number of 7 digit natural numbers are . (Exclude numbers starting with 0).

Thus the required probability is

b) The number 2 is present exactly 2 times, the number 3 is present exactly 3 times, the remaining digits are present no more than 1 time. The number of possible numbers with this feature is

From this number we have to subtract those numbers starting with 0. The number of such 7 digit numbers starting with 0 is

Thus the required probability is

orchestra answered 1 year ago

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