You can use tally() to get the frequency for every combination of groups.
library(tidyverse)
df1 <- data.frame(cat = c(1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4),
item1 = c(0,0,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,1),
item2 = c(1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0),
item3 = c(0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1))
df1 %>% mutate_if(is.numeric, as.factor) %>%
group_by(cat, item1, item2, item3, .drop=F) %>%
tally()
First convert your variables to factors then you can then use group_by(, .drop=F) %>% tally() to tally all of your variables, including all groupings with zero frequencies. Remove .drop=F to remove all zero frequencies.
cat item1 item2 item3 n
1 1 0 0 0 0
2 1 0 0 1 0
3 1 0 1 0 3
4 1 0 1 1 0
5 1 1 0 0 0
6 1 1 0 1 1
7 1 1 1 0 0
8 1 1 1 1 0
9 2 0 0 0 1
10 2 0 0 1 1
11 2 0 1 0 1
12 2 0 1 1 0
13 2 1 0 0 0
14 2 1 0 1 1
15 2 1 1 0 1
16 2 1 1 1 0
17 3 0 0 0 0
18 3 0 0 1 0
19 3 0 1 0 1
20 3 0 1 1 2
21 3 1 0 0 1
22 3 1 0 1 1
23 3 1 1 0 0
24 3 1 1 1 0
25 4 0 0 0 0
26 4 0 0 1 1
27 4 0 1 0 1
28 4 0 1 1 0
29 4 1 0 0 1
30 4 1 0 1 1
31 4 1 1 0 0
32 4 1 1 1 0
Alternatively, if that is too unwieldy, you can also try table1() from library(table1).
library(tidyverse)
library(table1)
df1 <- data.frame(cat = c(1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4),
item1 = c(0,0,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,1),
item2 = c(1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0),
item3 = c(0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1))
df1 <- df1 %>% mutate_if(is.numeric, as.factor)
table1(~ item1 + item2 + item3 | cat, data=df1)
To get a table of the frequencies and percentages. The top row is your cat variable.

table1() is really great for generating HTML frequency tables. Highly recommend. You can do lots of formatting and labels to make tables presentable. Here is a tutorial