Pregunta
14 A disc jockey (DJ) has 7 songs to play. Five are slow songs, and 2 are fast songs. Each song is to be played only once.
a) In how many ways can the DJ play the 7 songs if the songs can be played in any order?
b) In how many ways can the DJ play the 7 songs if the first song must be a slow song and the last song must be a slow song?
c) In how many ways can the DJ play the 7 songs if the first two songs must be fast songs?
a) If the songs can be played in any order, the DJ can play the 7 songs in 5,040 different ways.
(Type a whole number.)
b) If the first song must be a slow song and the last song must be a slow song, the DJ can play the 7 songs in 2,400 different ways.
(Type a whole number.)
c) If the first two songs must be fast songs, the DJ can play the 7 songs in
(Type a whole number.)
a) In how many ways can the DJ play the 7 songs if the songs can be played in any order?
b) In how many ways can the DJ play the 7 songs if the first song must be a slow song and the last song must be a slow song?
c) In how many ways can the DJ play the 7 songs if the first two songs must be fast songs?
a) If the songs can be played in any order, the DJ can play the 7 songs in 5,040 different ways.
(Type a whole number.)
b) If the first song must be a slow song and the last song must be a slow song, the DJ can play the 7 songs in 2,400 different ways.
(Type a whole number.)
c) If the first two songs must be fast songs, the DJ can play the 7 songs in
(Type a whole number.)
Ask by Bob Mcfarlane. in the United States
Mar 28,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
a)
There are 5,040 different ways to play the 7 songs.
There are 5,040 different ways to play the 7 songs.
b)
There are 2,400 different ways to play the 7 songs with the first and last being slow songs.
There are 2,400 different ways to play the 7 songs with the first and last being slow songs.
c)
There are 240 different ways to play the 7 songs with the first two being fast songs.
There are 240 different ways to play the 7 songs with the first two being fast songs.
Solución
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Como
Beyond the Answer
To determine the number of ways the DJ can play the songs for each scenario, let’s break it down:
a) If the songs can be played in any order, you can calculate this using the factorial of the number of songs: 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040.
b) If the first song must be a slow song and the last song must also be a slow song, you first choose the two slow songs for those positions. After placing the two slow songs, you have 5 remaining songs (3 slow and 2 fast) to arrange in the middle. The arrangement is 5! = 120 ways to arrange those. Then, since there are 5 choices for the first slow song and 4 choices for the last slow song, the total arrangements are: 5 × 4 × 5! = 5 × 4 × 120 = 2,400.
c) If the first two songs must be fast, there are 2 choices for the first fast song and once that’s chosen, only 1 choice left for the second fast song. For the remaining 5 songs (5 slow songs), you can arrange these in 5! = 120 ways. So, the total arrangements are: 2 × 1 × 5! = 2 × 1 × 120 = 240.
Thus, the final answers are:
a) 5,040
b) 2,400
c) 240
b) 2,400
c) 240
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