 Lv 1109 points

# blueishyacinth

• • ### Permutations and combinations?

(a) How many odd three-digit numbers can be formed from the digits 1,2,3,4,5,6 and 8 (each digit can be used once)?

(b) How many of the arrangements from part (a) are over 500?

• ### Permutations and Combinations?

A business has 4 vacancies for senior managers (each job has an identical description). 5 men and 3 women have applied for the positions.

If the 4 vacancies are filled at random, find the number of ways which contain at least 2 women.

• ### Permutations and combinations?

Eight boys and two girls sit in a row. If the girls do not sit together, nor sit on the ends of the row, in how many ways can the 10 people be arranged?

• ### Permutations and combinations?

You are given the digits 1,2,3,4 and 5 and the letters A,B,C and D. In how many ways can you arrange three of the digits and two of the letters? (Repeats are not allowed)

• ### Permutations and combinations?

There are 5 books and 4 magazines. In how many ways can 4 books and 2 magazines be arranged on a shelf?

• ### Position Vector?

Particle A is at the point with position vector (2 -5) at time t = 0 and moves with a speed of 10m/s, in the

same direction as (3 4).

Given that A is at the point with position vector (38 a) when t = 6s, find the value of the constant a.

• ### LCM and HCF?

The HCF of 56, x and 154 is 14 and their LCM is 4312. FInd the smallest possible integer x.

• ### Maths problem solving?

Five brothers, Abe, Brian, Cal, Doug, and Edwin, bought a car for \$42,000. Abe paid one third of the sum of the amounts paid by the other brothers. Brian paid one quarter of the sum of the amounts paid by the other brothers. Cal paid one fifth of the sum of the amounts paid by the other brothers. Doug paid one sixth of the sum of the amounts paid by the other brothers. How much did Edwin pay?

• ### Kinematics?

A particle, moving in a straight line, passes throught a fixed point O. Its velocity v ms^-1, t seconds after passing through O, is given by v=3e^(3t) + 4e^(-2t).

(a) Show that the velocity is never zero.

(b) Find, to the nearest metre, the displacement of the particle from O when t=3

• ### Algebraic Fraction?

An expression of the form:

(ax^2 – b)/ (cx^2 + dx – 1) simplifies to (3x + 4)/ (x + 2)

What was the original expression?

• ### Permutations and Combinations?

Calculate the number of four digit even number can be formed from the digits 3, 4, 5, 6 and 9 without repetitions.

• ### Permutations and Combinations?

Find the number of the arrangement of all nine letters of word SELECTION in which

i. The two letters E are next to each other

ii. The two letters E are not next to each other

• ### Permutations and Combinations?

A debating team consists of 5 students. These 5 students are chosen from 4 monitors, 2 assistant monitors and 6 prefects. Calculate the number of different ways the team can be formed if

i. There is no restriction

ii. The team contains only monitor and exactly 3 prefects

• ### Permutations and Combinations?

Diagram below five cards of different letters.

H E B A T

i. Find the number of possible arrangements, in a row , of all the cards.

ii. Find the number of these arrangements in which the letters E and A

are side by side .

• ### Special products?

Use the special products to evaluate the following:

(a) 433^2 - 432^2

(b)95 ^2

• ### Relative velocity?

A particle moving in a straight line, passes through a fixed point O with velocity of 14m/s. The acceleration, a m/s^2, of the particle, t seconds after passing through O, is given by a=2t-9. The particle subsequently comes to instantaneous rest, firstly at A and later at B, Find the distance AB.

• 