1. Find the number of ways the letters of the words FURTHER can be permuted.
2. Five different objects are spaced out evenly round a circle. In how many ways can they be arranged?
3. Seven students were late to a class. In how many ways can they occupy?
a. Three available vacant seats
b. Nine available vacant seats.
4. Find the number of times the word LAGOS can be permuted.
5. Find the number of ways the word MATHEMATICS can be permuted.

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )