5 boys and 6 girls attend a birthday party and play pin the tail on the donkey. If a girl wins first and second place and a boy wins third place, How many different arrangements of first, second, and third are there? =

75 Arrangements

Step-by-step explanation:

Girl can secure 1st & 3rd, boy can secure 2nd position in : 6 x 5 x 5 = 150 ways ; As :

The arrangement of first, second & third  :

It is same : If Girl G1 gets first rank & Girl G2 gets third rank, is same as ; Girl G1 gets third rank & Girl G2 gets first rank. So, two are considered the same group. Hence, number of arrangements are 150 / 2 = 75  arrangements.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204