Homework help needed [Base number, set and probability ]

1) The number 123456789(10)(11)(12)(13)(14) is written in the base 15. If convert the number to base 10, it is equal to 1 × 1513 + 2 × 1512 + 3 × 1511 + ….+ 13 × 15 + 14 What is the the remainder upon dividing the base 10 number by 7?

How am I able to find out the remainder when the number is so big?? Please explain the working so that I understand it

2) Given that A = {a: a is integers}and B = {b: b is integers}where

1/a + 1/b = 1/14

Evaluate n(A × B).

how do I start the calculation so that i am able to find out the total number of choice for a and b??thanks

4) A pack of 8 distinct cards is shuffled randomly. What is the probability that at least one of the cards remains at the same place after the shuffle?

5) How many 10-digit quaternary (base 4) numbers (leading zeros are allowed) consist of

(a) exactly four 1s?

(b) exactly two 2s and three 3s?

(c) at least two 0s?

6) From where he stands, one step toward the cliff would send a drunken man over the edge. He takes random steps, either toward or away from the cliff. At any step his probability of taking a step away is 0.75, of a step toward the cliff is 0.25. What is his probability of escaping the cliff?

7) In a chess tournament, a contestant received 1 point for a win, 0.5 point for a tie. Two Accounting students entered a chess tournament otherwise composed of Computing students. Each contestant played once against each other contestant. The two Accounting students obtained a total of 8 points, and each Computing students scored the same number of points as his coursemates. How many Computing students participated in the chess tournament?

please explain how do you guys got the answer thanks!

Re: Homework help needed [Base number, set and probability ]

Please do not post more than two problems per thread. One problem is preferred. I recommend opening new threads for problems 4) — 7). (By the way, where is problem #3?)

Quote:

Originally Posted by

**wong93** 1) The number 123456789(10)(11)(12)(13)(14) is written in the base 15. If convert the number to base 10, it is equal to 1 × 1513 + 2 × 1512 + 3 × 1511 + ….+ 13 × 15 + 14 What is the the remainder upon dividing the base 10 number by 7?

I do not recognize the pattern in 1 × 1513 + 2 × 1512 + 3 × 1511 + ….+ 13 × 15. It seems that the kth term is k × (1500 + 14 - k). But then the last term should be 13 × 1501, not 13 × 15.

Quote:

Originally Posted by

**wong93** 2) Given that A = {a: a is integers}and B = {b: b is integers}where

1/a + 1/b = 1/14

Evaluate n(A × B).

Does n(A × B) denote the number of elements in A x B? In any case, A and B are not well-defined. You cannot write a condition like 1/a + 1/b = 1/14 outside the curly braces in the set-builder notation. Either A = {a: a is an integer}, period, and then 1/a + 1/b = 1/14 is not allowed because the definition of A is finished and it is not clear what *a* is anymore, or A = {a: a is an integer and 1/a + 1/b = 1/14}, which does not work either because it is not clear what *b* is.