A division director is planning a presentation divided into

Question

A division director is planning a presentation divided into seven 10-minute blocks. Each of the four product managers will speak for 10 minutes each, and the director will speak for the remaining 30 minutes, but no more than 10 minutes at a time.

How many different speaking orders are possible?

(A) 120
(B) 144
(C) 192
(D) 240
(E) 840

How many different speaking orders are possible?

(A) 120
(B) 144
(C) 192
(D) 240
(E) 840

AdarshSambare · Answer

There are 7 speaking blocks of 10 minutes each.
 
 The 4 product managers each speak once, so they occupy 4 blocks. 
 The director speaks for the remaining 30 minutes. Since the director cannot speak for more than 10 minutes at a time, the director must speak in 3 separate 10-minute blocks.  
So the 7 blocks are:
 
 4 distinct product managers 
 3 identical director blocks  
The number of ways to arrange these 7 blocks is:
7! / 3! = 5040 / 6 = 840
Therefore, the number of different speaking orders is  840 .
 Answer: (E) 840 .

Samrath19 · Answer

Consider Product Manager blocks as P1 P2 P3 P4
Consider Director blocks as D D D (identical)

D D D must be separated by at least one Product Manager block (Director speaks no more than 10 mins at a time)

P1 P2 P3 P4 can be arranged in 4! = 24 ways

Slots for Director can be visualized as: __ P1 __ P2 __ P3 __ P4 __

This is like selecting 3 out of the 5 available slots for the Director. So Director can be placed in 5C3 = 10 ways

Total ways = 24 * 10 = 240

BongBideshini · Answer

Let the four product managers be P1, P2, P3, and P4.
The director must speak for 30 minutes total, but in blocks of at most 10 minutes. Since each block is 10 minutes, the director occupies exactly 3 of the 7 blocks.
So the presentation consists of:
 
 4 distinct product-manager blocks 
 3 identical director blocks (D)  
We need arrangements of P1, P2, P3, P4, D, D, D with one extra condition: The director may not speak for more than 10 minutes at a time.
Therefore no two (D)'s can be adjacent.

The four managers can be ordered in 4! = 24 ways.

After arranging the managers, there are 5 gaps:
_, P, _, P, _, P, _, P, _

The 3 identical (D)'s can be placed in any of the 5 gaps
So, 3 gaps for (Ds) can be selected by 5C2 ways

Total arrangements = 24 x 10 = 240

Answer: (D)

A division director is planning a presentation divided into

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A division director is planning a presentation divided into

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards