1.How many four-digit numbers can be formed with the 10 digits 0, 1, 2, 3, . . .,1 answer below »

1.How many four-digit numbers can be formed with the 10 digits 0, 1, 2, 3, . . ., 9, if (a) repetitions are allowed, (b) repetitions are not allowed, and (c) the last digit must be zero and repetitions are not allowed?

2. Four different mathematics books, 6 different physics books, and 2 different chemistry books are to be arranged on a shelf. How many different arrangements are possible if (a) the books in each particular subject must all stand together and (b) only the mathematics books must stand together?

3. Five red marbles, 2 white marbles, and 3 blue marbles are arranged in a row. If all the marbles of the same color are not distinguishable from each other, how many different arrangements are possible? Use the EXCEL function ¼MULTINOMIAL to evaluate the expression.

Dec 16 2020 01:08 PM

1 Approved Answer

richard m
answered on
December 18, 2020

5
Ratings,(24 Votes)

SOLUTION

1.How many four-digit numbers can be formed with the 10 digits 0, 1, 2, 3, . . ., 9, if (a) repetitions are allowed, (b) repetitions are not allowed, and (c) the last digit must be zero and repetitions are not allowed?

(a) repetitions are allowed

Since the first digit of a number caanot be zero, for the first digit we have 9 possibilities

For the second, third and fourth digits there are 10 possibities for each

## 1 Approved Answer

December 18, 2020SOLUTION

1.How many four-digit numbers can be formed with the 10 digits 0, 1, 2, 3, . . ., 9, if (a) repetitions are allowed, (b) repetitions are not allowed, and (c) the last digit must be zero and repetitions are not allowed?

(a) repetitions are allowed

Since the first digit of a number caanot be zero, for the first digit we have 9 possibilities

For the second, third and fourth digits there are 10 possibities for each

The four digits formed are 9 x 10 x 10 x10 = 9000

(b) repetitions are not allowed,

There are 9...

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